Which one allows me to do more customization? I know that there are lots of templates for Perstashop and thats a plus. What are other main differences?
Prestashop because it has very nicely done documentations, large community forums, hundred and thousands of third party theme providers. You can consider opencart as well, it offers a product filter option inbuilt (filter by price, color, weight etc) which i believe prestashop is not offering without extension.
The question which one is better is too vast to answer. It may be possible to argue none of them are any good. Each solution will have its own merits. You need to analyze exactly what your requirements are and then make some perfect inference on your future needs to figure out what is best for you.
Prestashop = open source, big commerce = propriety. period. I guess you get it. Besides, as far as I know, bigcommerce is only good for facebook sales?! If this is what you want, Prestashop does have a facebook catalog module. PS is very customizable. Just see its themes. Hope this helps.