It all depends with what you're cutting. I can bog down my 4400 with a 6 foot cutter in the right stuff. Trying to cut deep, thich clumps of fescue at a low setting is much harder than going through brush and brambles.
I think the 3400 will handle a 6 footer just fine in most situations and if the stuff is too deep, like someone said, overlap a little or raise the mower a bit.
Like someone said, a mower wider than your tires can have advantages, but it also has drawbacks. I like that my 6 footer fits within the wheel width; makes working in tight places a lot easier.
Whatever you do, if you go to a medium duty mower or any heavier unit, the problem is not so much if the hp is sufficient to turn it but if your 3 pt lift capacity is sufficient. Check the specs in your owners manual. It will give you a max weight specifically for a mower. You can't just go by the specs of the 3 pt lift capacity.