In our GEM survey in Thailand, we are asking this question (innovation related to product, to services, to manufacturing). We find that in start-ups and especially in young businesses, women tend to be consistently more innovative than men. There is a difference when it comes to the sector they work in. See the paper from the ICIE proceedings "An Empirical Investigation of Gender Impact on Technological Innovativeness Among Thai Entrepreneurs via GEM Database" on my researchgate page. Hope it helps.