[Sohcahtoa82]

100% this

On rare occasions, using a 3rd party site will net you a better deal, but often, it's the exact same price, or a price within just a few dollars.

But if your reservation has a snag of any kind, you're basically fucked. The hotel will tell you to talk to Booking, Booking will tell you to talk to the hotel, if you can even talk to anybody.

I'd rather spent the extra dollars and book directly and just not have that worry.