The World Health Organisation reports the observed rate of vaccine reactions from each of sixteen different classes of vaccinations. It divides each type of reaction into mild adverse events or severe adverse events.
For HPV in particular, it offers statistics for quadrivalent (i.e. protecting from four variations of HPV) and bivalent version of the vaccine. I quote from the quadrivalent version that seems to have more reactions.
There are a number of possible reactions. Mild reactions are common, including pain at the injection site (83% of patients) and headaches (26%). Serious reactions are much rarer, with anaphylaxis occurring 0.00017% of the time.
Compare that to BCG, and we find more occurrences of mild reactions with papules (lumps), mild ulcerations and/or scars occurring in "almost all vaccinations". There are also more occurrences of severe reactions, with local abscesses, infections and similar occurring in 0.01-0.1% of the time, osteitis (bone inflammation) occurring up to 0.03% of the time and Immune Reconstitution Syndrome occurring 0.00016% of the time (amongst other severe adverse events).
10% of the Rubella portion of MMR vaccines leads to serious reactions - acute arthritis. Fortunately, it is generally short-lived:
Symptoms typically begin 1-3 weeks after vaccination and last one day to three weeks.
In conclusion, BCG has more occurrences of both mild and severe reactions than HPV vaccines, while MMR vaccines have much more occurrences of severe reactions than HPV vaccines.
Note: This should not be read as an argument not to get vaccinated, as the risk of the diseases is considered higher. However, it is an argument against people who overstep the science when they claim that vaccines are "100% safe".