My reply probably won't be especially helpul, but I thought I'd add it anyway and give the thread a bump...

I didn't look into WooCommerce, but I did sign up for the 14 day free trials for Big Commerce and Shopify recently, which I initially thought would be enough to expolore both at the same time and decide in the best one to go with (it wasn't  but if you do one trial at a time, you should have a decent opportunity to explore options and functions).

I ended up asking another group of sellers for their recommendations, and although I didn't get a high quantity of answers, Shopify was the more popular, with eBay integration being among the benefits cited and it's what I decided to go with in the end. I can't really speak for the integration or inventory management, though, as I do that sort of thing manually to ensure there is 0 chance of error or overselling (eg I list 40% of stock on one site, 40% on another, and keep the remaining for cases where I may need to replace something, or to update stock levels on whichever site sells out first.