Hiya, we have both - I bought a reclining chair with a tray for my first son, and now that he is 1.5 we bought him a tripp trap and given the reclining chair to his little brother - now 5.5 months and weaning.
I can see the good and bad for both chairs. I wouldn't put a 5.5 month old in a tripp trapp. I don't think it's very comfortable for little ones and they need to be able to sit up really well. He'd slip down for sure. A tray is pretty good I think for younger babies, a bit less messy and easier to clean, it goes right up to their tummy so less food on the floor. The reclining bit was very useful when our oldest son was old enough to hold his bottle / beaker of juice or milk and it happened many times that he fell asleep in it and we just reclined the back and he had nice naps. Couldn't do that with a tripp trapp.
However, now that our oldest son eats really well, the tripp trapp is wonderful. We and he love it!
Bought it from this website: www.backinaction.co.uk
And the reclining highchair we bought from Argos. We chose one that had a bar between the legs, it's good for younger babies as they can't slip down.It's the Chicco Polly highchair.