Having watched the two extremes recently, Rinne at 6'6" and Saros at 5'11", the difference is, well, pretty big?
Saros is very smooth, he always seems to be where he should be. His angles are really good, and his agility is insane. His downsides are that because he is smaller you will get some of those crazy bounces and tips that would catch a taller goalie in the shoulders going in. Obviously more room to shoot up top as well. His glove isn't anything special and his rebound control can get a little nasty, especially to start the season.
Rinne was much more choppy, more of a fish out of water. He was athletic but it didn't show up in smoothness. Now as he got older that got better, he settled down much more in his later years and did become much more smooth. His ability to move the puck was much better than Saros and his glove hand was so good it could actually get him into trouble. He tried to catch everything early in his career.
I'd say the advantage being big gives you is that you don't need to be as precise. When you are smaller you gotta be agile and things like angles need to be dead on or you will just leave even more space for shooters.