In the US, more people have died of COVID-19 in hospitals* (ca. 82,000) than in all other locations (ca. 48,000) from February 1 to July 18, 2020. However, as you surmised, this is the case for many conditions. Hospitals were the single most frequent location of death for respiratory diseases in general (2,3 out of 4,9 million in 1999-2018), as well as for deaths from any cause (17.3 million out of 50,6 million; both stats from the CDC).
And, as you also surmised, it stands to reason that people with mild symptoms are less likely to either be hospitalized or die from COVID-19. The CDC states:
Among all patients, a range of 3% to 17% developed ARDS compared to a
range of 20% to 42% for hospitalized patients
Patients with a mild clinical presentation (absence of viral pneumonia
and hypoxia) may not initially require hospitalization, and many
patients will be able to manage their illness at home. The decision to
monitor a patient in the inpatient or outpatient setting should be
made on a case-by-case basis. This decision will depend on the
clinical presentation, requirement for supportive care, potential risk
factors for severe disease, and the ability of the patient to
self-isolate at home.
Some patients with COVID-19 will have severe disease requiring hospitalization for management.
Thus, it is correct to say that, to date, more people who have died from COVID-19 in the US have done so in hospitals than at home. However, this does not mean that a specific patient is more likely to die from COVID-19 if transferred to a hospital; on the opposite, there have been studies showing that, for example, distance from an intensive care unit (ICU) increases the mortality rate.
*Note: I always take "hospital" to mean "inpatient"; if we include emergency rooms, the hospital numbers would be higher in all cases.