Chase is not a headache to deal with - it's only sometimes a headache getting the card in the first place. They are picky about who they'll approve, with their various unwritten rules about 5/24 and other credit behaviors they deem "risky".
But once you have the card(s), they are great! The travel rewards are incredibly flexible - my main airlines are Unites and Southwest, and the points transfer 1:1 to either one. Their travel portal is great for booking discounted hotels and rental cars with the points.
And the cards earn heaps of points, especially if you have several of them to work for you. Obviously CSR and CSP are the main workhorses, but the Freedom cards are great supplements. The sapphire cards are also great to use during travel - Excellent rental car policies, no FTF's, etc.
Chase is, for the foreseeable future, going to be my primary set of travel cards. Other banks offer similar (Amex, etc), but Chase works great for me so it's what I'll stick with.