For me, it's a two-phase kind of thing:[ul][li]Phase 1: Recon: Carefully survey the environment and see what my options are. Find out where my objectives are and how I should get to them. If the alarm sounds at any point, go to Phase 2. Otherwise, maintain this as long as possible. An example would be the typical Harvest & Trustee "Bank Heist" in Payday 2, where despite the fact that I intend to fight my way through the heist in loud, I try to stealth as much as I can to have the drill mounted before the alarm sounds, and maybe have the security room neutralized before I get the drill running if I can.[/li][li]Phase 2: Assault: Now that I know my objectives and my options on how to get to them, it's time to kick ass and chew bubblegum... And I'm all out of gum. Basically, get shit done and bulldoze my way through every enemy that tries to stop me. Referring back to the PD2 "Bank Heist", once I get the drill running it's time to make some noise. Sometimes, if I find the route to do it, I'll get the drill running THEN use Shaped Charges to blast into the security room, with the explosion setting off every alarm in the bank. At that point, it's just a matter of survival; and that's usually going to mean killing everything that tries to stop me from emptying that vault.[/li][/ul]
Though honestly, in general? Shoot first, ask questions later. Sneaking around is usually boring anyway. Or it's tense, but not in a way that I enjoy.