tundra then a bettER choice?

First decide how much truck you need for your new TT, and that means more than tow ratings. A 30' TT can weigh 6000-12000 pounds. A typically equipped half ton pickup may or may not handle 6000 pound TT, and none can handle a 10k loaded TT. The Tundra along with any other half ton should be carefully researched as a match with a potential TT. Receiver ratings and payload are often exceeded well below tow ratings. Meanwhile, nearly any current model 3/4+ ton can tow nearly any travel trailer, so then it's a matter for which model you like best and gas vs. diesel.

As far as reliability, Ford/GM/Ram sell far more full sized trucks than Toyota, like 2 million compared to 120k per year. If any of them had issues, the sales would not be so skewed. None of them should be avoided specifically for reliability.