Simply, the K361 seems to be a slightly brighter K371, which allows a bit more light into the bass range, uncovering a bit more detail. The sub-bass is not as strong as the 371 but it is a nice even-keeled presentation. Given the choice, I'd take the 371 for it's overall balance and solid bottom. If I had no choice, I'd take the K245 over both...it seems to incorporate the strong points of the 361 and 371 in one package. Less comfortable than 361/371 but it doesn't have the seal inconsistency of those.
So, as always, it's a matter of taste and preference. But inexpensive enough to take a chance without really being disappointed.
Very cool to see you mention the K245 in relation to the K361/K371 and in a favorable light. I picked up the K245 for $50 used and I’m trying to maintain the discipline not to have to get the K371.