Both platforms have an excellent reputation and a lot of ways to buy and sell Bitcoins.
It's up to you if you're looking for multiple options, I recommend LocalBitcoins, if you want a quick response and specific transactions without you being scammed, Paxful is the best.

I have tried them and through my experience, I prefer LocalBitcoins because they offer a lot of options for buying and selling in addition to plains of transactions.