Randy did a threat on modding the 355T with some pics of the internals and by his book it is a well designed engine. By all accounts, and I have owned a 355T, they run well and are great value. Some of the climbers here will say that they preffer the 200/201 design over the echo for durability. Chris (kenjaxtree) noted that his 355T had lots of broken plastic on it. Keep in mind, echo parts may be priced to be replaced, than priced to replace the saw. Also the durability reports come from pro climbers subjecting their tools to more use. Nothing broken on my saw and it ran great with a muffler mod and limiters trimmed, I also advanced the ignition 6 degrees, for better throttle response.
As far as the construction, it has a stuffed crank, looks like forged three piece, transfer tunnel inserts, and a domed piston, non cat muffler, and adjustable carb. Echo post the IPL on there website. The euro equivalent of the 355T is the 360TES, and I believe it has a cat muffler. It gets good reviews.
As for the 361P, like previously mentioned a rear handled 355. The price point reflects the low demand and volume for these saws. One of the dealers on here mentioned he had some run time on it and said it accelerated better than the 355T. It has a different coil.
Cheers