I'm a firm believer in both systems and feel when it comes to kicking/banking. When I was playing 3 cushion a ton, I learned a lot about cueball and object ball reactions just from banging the balls around while learning. I also learned dozens of systems to help estimate all sorts of shots - normal 3 cushion shots, 2 rail umbrella systems, dead ball systems, etc. Many of these are useful in pool as well, and I use them all the time.
Ultimately though, you will need to understand how hitting the cue ball with different speeds and spins affects the lines, as well as how table conditions do the same. When you combine the system knowledge with the "feel" knowledge and learn to have confidence in it then you will no longer feel out of sorts when staring down a shot in competition.
I remember learning the Corner 5 3 cushion system. Even though it's simple math (CB - third rail = first rail), memorizing the track lines and rail numbers, learning to estimate cue ball positions, etc. takes some time. I would spend 30 seconds or more over a shot trying to figure it out. But with just a bit of practice you can reduce that to 1 - 2 seconds, almost seamless, not to mention over time you build up quite a bit of intuition based on all of the system shots and you can just see the lines easily.
No substitute for practice. Focus on a few systems at a time, dedicate time to each one during each practice session until they become ingrained, and you won't have that feeling of losing confidence during a game. Worse case you miss and figure out where you went wrong - bad calculation, bad stroke, didn't account for conditions, etc.
In case you want some more reference materials, I did a series of articles years ago, they can be found at poolstudent.com, just go down the right side to the Instruction link. You'll find multiple methods for 1 and 2 rail kicks and a write up on System Sid. Someday I'll finish what I started...
Scott