True.
Says the WHO since March 2020:
Children are important drivers of influenza virus transmission in the community.
For COVID-19 virus, initial data indicates that children are less affected than adults and that clinical attack rates in the 0-19 age group are low. Further preliminary data from household transmission studies in China suggest that children are infected from adults, rather than vice versa.
While the range of symptoms for the two viruses is similar, the fraction with severe disease appears to be different. For COVID-19, data to date suggest that 80% of infections are mild or asymptomatic, 15% are severe infection, requiring oxygen and 5% are critical infections, requiring ventilation. These fractions of severe and critical infection would be higher than what is observed for influenza infection.
Those most at risk for severe influenza infection are children, pregnant women, elderly, those with underlying chronic medical conditions and those who are immunosuppressed. For COVID-19, our current understanding is that older age and underlying conditions increase the risk for severe infection.
And true, show the most up to date statistics from the CDC, if we concentrate on mortality:

— Deaths involving coronavirus disease 2019 (COVID-19), pneumonia, and influenza reported to NCHS by sex and age group. United States. Week ending 2/1/2020 to 11/7/2020. on: "Weekly Updates by Select Demographic and Geographic Characteristics. Provisional Death Counts for Coronavirus Disease 2019 (COVID-19)", cdc.org
When comparing these numbers it should be noted:
It is extremely remarkable that in 2020 influenza testing was as ever further increased, but the flu season was much lower than expected, with the southern hemisphere even skipping the flu season entirely:
Globally, despite continued or even increased testing for influenza in some countries, influenza activity remained at lower levels than expected for this time of the year. In the temperate zone of the northern hemisphere, influenza activity remained below inter-seasonal levels, though sporadic influenza detections were reported in some countries.
In the temperate zones of the southern hemisphere, no influenza detections were reported across countries.
— WHO: Global Influenza Programme — Influenza update - 380 — 09 November 2020, based on data up to 25 October 2020
Meaning the CDC table may show a somehow inflated number of covid deaths due to counting and reporting issues, but the also slightly imprecise numbers for influenza deaths are also much lower than usual currently.
Similarities:
Both COVID-19 and flu illness can result in severe illness and complications. Those at highest risk include: Older adults, People with certain underlying medical conditions, Pregnant people,
Differences: The risk of complications for healthy children is higher for flu compared to COVID-19.
Influenza is dangerous for children but the current mortality rate for Covid in children is almost 0.0%.
Or, in the words of a trustworthy state public health agency:
Children are not considered to be at risk of serious illness
Even if they have one of the conditions or illnesses that increase the risk for adults and older people, children are very unlikely to become seriously ill.

— Our World in Data: Mortality Risk of COVID-19
But this may still change. While the above numbers still hold true for the vast majority of countries in Europe, for example Sweden and Germany, there appear some statistical outliers. While for influenza the attack rate in younger patients is generally much higher than for coronavirus, in influenza we also see the severity changing according to location, season and virus subtype.
For England – in this year – and note that the infinitesimally small number stats for children are within the group "<65"
COVID-19 mortality rates were higher than influenza and pneumonia rates for 2020 and the five-year average for all age groups in England

Age-standardised and age-specific mortality rates for deaths due to influenza and pneumonia, and COVID-19, England, occurring between 1 January and 31 August 2020 and registered by 5 September 2020
- Deaths due to coronavirus (COVID-19) compared with deaths from influenza and pneumonia, England and Wales: deaths occurring between 1 January and 31 August 2020 Comparison of deaths from the coronavirus (COVID-19) with deaths from influenza (flu) and pneumonia. Includes deaths by date of death occurrence and breakdowns by sex and age.
For New York City alone we see in a comparison for strong flu seasons and covid:
Notwithstanding the substantial burden of less severe infections due to both influenza and COVID-19 in different age groups, and the possibility that risk of death may vary over time, the higher age-specific mortality in the young in both the 1918–19 and 2009 influenza pandemics compared with COVID-19 is an important factor for decisions about whole-of-population versus age-targeted vaccination strategies.
— David J Muscatellod & Peter B McIntyred: "Comparing mortalities of the first wave of coronavirus disease 2019 (COVID-19) and of the 1918–19 winter pandemic influenza wave in the USA", Int J Epidemiol. 2020 Sep 15. doi: 10.1093/ije/dyaa186
In summary:
- People <65 years old have 16–100 fold lower risk of COVID-19 deaths than older people.
- Age risk gradients are less steep in India and Mexico.
- Absolute risks of COVID-19 in the population are low for people <65 years old.
- COVID-19 deaths occur sparsely in people <65 without underlying conditions.
People <65 years old have very small risks of COVID-19 death even in pandemic epicenters and deaths for people <65 years without underlying predisposing conditions are remarkably uncommon. Strategies focusing specifically on protecting high-risk elderly individuals should be considered in managing the pandemic.
COVID-19 may thus be yet another disease with a profile dependent on inequalities and generating even more inequalities. The difference in the proportion of deaths in people <65 years old across different US locations may be due to chance, or may reflect genuine differences in the proportion of deaths occurring in nursing homes and/or the proportion of deaths occurring in younger populations of disadvantaged people, differences in reporting of COVID-19 deaths, or other unclear reasons.
Of interest, influenza deaths seem to have a similar difference in age distribution between the USA and European countries like Italy: a larger proportion of influenza deaths in the USA tend to be in the <65 age group (Estimated Influenza, 2018), as compared with Italy (Rosano et al., 2019). Of course, a major difference between influenza and COVID-19 is that the latter typically does not cause deaths in otherwise healthy children, in contrast to influenza (Wang et al., 2020b).
— John P.A. Ioannidis & Cathrine Axfors Despina G. Contopoulos-Ioannidis: "Population-level COVID-19 mortality risk for non-elderly individuals overall and for non-elderly individuals without underlying diseases in pandemic epicenters" Environmental Research, Volume 188, September 2020. doi
Influenza is least dangerous for young adults, but more dangerous for children and elderly people.
Influenza virus accounted for 7% of ALRI cases, 5% of ALRI hospital admissions, and 4% of ALRI deaths in children under 5 years. About 23% of the hospital admissions and 36% of the in-hospital deaths were in infants under 6 months. […]
A large proportion of the influenza-associated burden occurs among young infants and in low-income and lower middle-income countries.
— Wang et al.: "Global burden of respiratory infections associated with seasonal influenza in children under 5 years in 2018: a systematic review and modelling study", Lancet Glob Health 2020; 8: February 20, 2020, doi.
US Mortality (42 states and NYC reported):
Children were 0.00%-0.18% of all COVID-19 deaths, and 16 states reported zero child deaths
In states reporting, 0.00%-0.13% of all child COVID-19 cases resulted in death
— Children and COVID-19: State-Level Data Report, AAP Report Nov 2020
While the CDC reports around 200 yearly influenza deaths in children with an estimate of 600 'true' cases due to underreporting (CDC Flu & Young Children), with actual data for 2020 still listed as insufficient:

— Influenza-Associated Pediatric Mortality, CDC FluView
That is: for the start of the year we saw some pediatric influenza deaths (a 'record' of >170 for season 19/20) but for the season that just started now we have today:
"No influenza-associated pediatric deaths occurring during the 2020-2021 season have been reported."
That makes the other initial claim of 'more very young persons died so far from flu than from covid' true: while the 'everyone now has corona' season of 2020 so far within the age bracket of 0–24 had a reported death toll of covid deaths excluding inluenza (table 1) at 155, in the US the overall very mild flu season of 2019/20 took the lives as reported of finally in week 38 at 188 pediatric deaths (Compared for example to 2009 influenza-related pediatric deaths of even 317). Meaning a low prevalence influenza took more young lives in absolute numbers than the high prevalence corona outbreak. That well may change for the absolute numbers, since flu seems to remain at very low activity compared to corona which remains at a somewhat higher activity level. But the relative risk is unlikely to change: at similar virus activity the flu is more dangerous than corona for children.