Some laptop have performance upgrades depending on their size, MacBooks I believe fall in that category.
Other then that, no, it doesn't. If you take a look at two laptops with the same specs but differentiate in size, then no, it will not alter or effect the performance, why should it? The notable diffrence is ofc the size and inches added to your screen. For your final question, you need to see what suits you better, 17 inches will provide a bigger picture (consdering how it's bigger ofc) which is well suited for gaming, media related stuff like moves and photoshopping if that's your preference, then by all means, go for it. If you take your laptop with u like everywhere, the smaller the better IMO.
