My rule of thumb is never, ever book through a third party unless you have a very good reason to.

The huge difference (mostly relevant if you have status) is that you have to go through an intermediary to get any help with your reservation. In recent months, UA has gotten even more strict about this. I know the rules, I can get to the 1K desk quickly, so having a third party in the middle is a big hassle that I have absolutely no need for. jsloan notes more of the specifics, but it basically means I know what is going on with my ticket at all times. No OTA has customer service worth even 1% of what I get from the 1K line. IIRC some categorization of credit cards requires "purchased directly from airlines", too.

Obviously, I have to fly on agency tickets sometimes - redeeming various reward points for cash travel, etc. I try very hard to make these non-stop domestic journeys where nothing could possibly go wrong.