I'm not having that problem. At this point (Level 25) I'm feeling pretty OP with stealth.
I have 4 ranks in the Sneak Perk, I've collected 4 Covert Operations Manuals, and I wear clothing, not armor. I use a Suppressed 10mm Pistol 90% of the time. I have 3 Ranks in Gunslinger, and 2 Ranks in Ninja, plus 1 Rank in Sandman (which gives you a +15% damage to Sneak attacks with suppressed weapons).
I just cleared out a Super Mutant camp without every going into DANGER. I cleared out 2 buildings full of Triggermen without triggering DANGER. Remember that CAUTION does NOT mean you have been discovered, they just know something is wrong and are searching for you. If you are patient and wait until an enemy is alone, and you can take them out with one shot, you don't even trigger CAUTION.
As for how well stealth and sneaking is working - I just had a mutant hound walk in a circle around me, and SHOVE me out of the way, and it never detected me. I was in CAUTION.
My advice to you is not to consider CAUTION a failure state. It isn't like in Fallout 3 or Skyrim. Sneak Criticals still work from CAUTION, and enemies shooting at you during CAUTION are not shooting at you, they are shooting in the direction of the shot. Move and they'll keep shooting the same area, and you can shoot them in the back.