We had a 34-footer for 6 years (and towed it with a 1/2 ton, BTW). The trailer was all the truck could handle - not from the engine's standpoint but the truck body is just a bit light for that size TT (GVWR of the TT was 7600, so lighter than what you're considering). Backing was difficult when turning into a campsite - I got lots of practice as our driveway was a 90-degree angle from our road, and the narrow road didn't allow a lot of space for everything to happen. Got it figured out. Backing eventually became, if not easy, not too bad - that size TT doesn't act as squirrely as something smaller when backing, which is nice.
On the road, we noticed a lot of wind wag. Not really sway, per se - our Equal-i-zer handled it well - but the trailer being so long and quite tall, really caught the wind and we always felt the tail was wagging the dog a bit on windy days.
Handling wasn't one of the issues that led to our downsizing (our current TT is 27' and a better match for our truck), but there were plenty of issues with a big trailer - it doesn't fit in many state park & national forest campsites, which was probably the biggest problem for us. We got tired of camping almost exclusively in private CGs, cheek to jowl with others.