CDC report on anaphylaxis (serious allergic reaction) when two vaccines were given:

Pfizer-Biontech 2 million first doses: adverse reactions 0,2%.
21 cases of anaphylaxis occurred, 90% in women, median age 40. Onset within 13 minutes and 71% within 15 min. 14% within 30 min and 14% after 30 min. No deaths.

Moderna vaccine had 10 cases of anaphylaxis among 4 mill receiving first dose. Mostly within 15 min.
Other allergic reactions were similar in the two groups.

Reference: Journal Watch march 2021