One person with influenza spreads it to 1.3 people, on average. If mitigation measures bring that below 1.0, it slows down. We may have wiped out some influenza strains entirely (https://arstechnica.com/science/2022/09/covid-may-have-pushe...).

One person with COVID's early strain spreads to 2.9 people, and that was with massive societal mitigation measures in place.

Omicron's is listed as a whopping 9.5. Some of that likely includes reduced mitigation, but it's still enormous.

It's clearly substantially more infectious. Three generations of spread at 1.3 mean ~2 people infected; three generations at 9.5 mean ~850 people.

The Flu is/was suppressed by the measures more because its lower R0 was pushed down closer to 1 which prevented any exponential expansion that is commonly happening when people don't care (i.e. don't wear masks, socialize more and are lax about washing their hands).