Sure thing.
I guess the first place I would start is with the most indisputable evidence, which is numbers based: voter participation and women's representation. With both of them, you can essentially draw a line from first past the post to.... We'll start with voter participation. First past the post has had turnout averages in OECD countries over the last 30 years of just under 60%. We don't really have data for AV systems, because Australia has mandatory voting, but in PR systems it's 68% for list PR, 76% for MMP, and 70.4% for single transferable vote. These are stats from OECD countries over the last 30 years, with mandatory voting countries removed, so there are no incentives and penalties behind it.
For women's representation, simply stated, PR systems have more representation of women. I think the best case to look at is Australia, where they use two different systems, one for the senate and one for the House of Representatives. The senate uses STV, and the House of Representatives uses alternative vote to elect their representatives. Since that's been the case, there's been consistently about a 10% difference, from 25% in the House, to 35% or so in the the senate in recent years, for the number of seats held by women. That's huge.