I'd suggest a 3-tiered system. Numbers are purely for example
1.) Automatic-detection Vision Cone (~20-ft cone) - unless you're invisible/blocked by an obstacle, the enemy detects you
2.) Stealth Check Vision Cone (extends another 20-ft past ^) - Your stealth check vs the enemy's passive perception
3.) Stealth Check Hearing Radius (radius of maybe 30 feet) - Your stealth check vs the enemy's passive perception
The latter two options could be slightly modified to be harder or easier. And any/all of the detection areas could be visible or invisible, though it'd probably be least confusing if either all were visible or all were invisible. But as others say above, the important part of this suggestion is that stealth checks are now rolled - an 8-DEX fighter in plate armor can't freely sneak up to/past an enemy.
Imo, essentially nothing besides tactics should be player-skill based in a turn-based D&D rpg, so I'm not a fan of introducing player skill into stealthing.
