Will I notice much difference beside just having a slightly longer cockpit between my seat and fork if I upgrade from a 50mm to a 65 mm stem? is this 15mm a significant enough adjustment to make my climbing or downhill riding feel any different? In what ways?
Changing from 50 to 65 (or the opposite) is definitely noticeable. And depending on your needs, switching may improve your riding.
Switching from 50 to 65 will mean more pressure on the front end. That means better cornering (the front end will not wash out easily) and more stability on the downhill. Some people also mention that it'll improve climbing on difficult terrain.
Switching from 65 to 50 will improve the agility of the bike. You'll be able to bunnyhop, manual and trick your bike easier and with less effort. You'll also have a slight advantage at very very steep technical downhill trails. It'll also make your cornering snapier but be careful of wash outs. A switch of this type is also paired with an increase in bar width.