No doubt the 350 is an excellent saw. I'm surprised to hear you say it out cuts the 346. Seems the 346 should beat the 350 in every condition, except possibly a full buried cut, and I would have thought it would win there too. I often run mine with a 20" bar, but it slows down considerably on anything over 14" diameter. It will sink into oak with the 20" bar, but a bigger saw is much more graceful. I also like the rim sprocket set-up on the 346, but to your point, it isn't much of a benefit if you don't cut a lot of wood and need to change them out. I've worn out about 5 chains and my current rim sprocket and still looks almost new.
My 346 is a breeze to start; two pulls with choke on to make it pop, 1 pull with the choke off to start it. Once it's warmed up it starts the first pull.
I would think the Dolmar 5100 would be the best competitor to the 346, but that's been argued about a million times. Seems to always come down to whether you want more power with slightly more weight (=> 5100), or better filtration, higher revs, and years of proven performance (=> 346xp). If I was choosing a single saw, I'd look seriously at the 5100. Since I have a 70cc saw for firewood and felling, I really like the "flickability" of the 346 and the way it slices through lumber like a knife. Truth is, they both seem to be fine saws. I do think a nice feature of the 5100 is the internal clutch, making changing chains and rims somewhat easier.
I've had the 346 for a while now and don't see a compelling reason to change. It's hard to imagine being happier with a purchase.