Having handled and shot both (I own a M36 and my dad owns a .357 LCR), I have to say that both are good guns and it's mainly a matter of personal preference. While the LCR's trigger is considerably lighter, it is also noticeably longer and has a very long reset. I personally find the M36 trigger, while heavier, to be smoother and, having primarily owned and shot S&W revolvers, much easier for me to get used to. I find the recoil with .38 +P ammo to be pretty comparable between the two, but the M36 would probably be more pleasant if I swapped out the factory stocks for something more hand filling (and the LCR would probably be much worse without its excellent Hogue Tamer grips).
While the LCR is lighter, I've not found the weight of the M36 to be a hindrance and I regularly pocket carry it (I've never even bothered to try any other method with this revolver.
As far as +P ammo is concerned, it can be safely fired in a vintage M36 but I would only do so in moderation. I personally only shoot 50-100 rounds of +P per year through my M36 and restrict the majority of my practice to standard pressure ammo. As has been mentioned, +P ammo won't cause a KB in a M36 (unless the ammo is grossly overpressure) but it will cause accelerated wear with regular use. Also, my M36's sights seem to be regulated for 158gr bullets while Dad's LCR seems to shoot to POA with lighter 125gr bullets.
Personally, I prefer the M36 but then again I've always been a S&W man. Both are fine revolvers and you cannot go wrong either way. I would suggest, if you decide on the LCR, that you get the .357 Magnum version. Not only does that version offer you more choices in ammunition, but the extra weight will also help to dampen the recoil of .38 Special ammunition.