Most people call about a tub for cosmetic reasons: it's stained, it's chipped, the finish has gone dull and chalky, or it's a color that was fashionable forty years ago. In almost every one of those cases the tub itself is structurally fine and reglazing is the obvious answer.
Reglazing strips the old finish, etches the surface so the new material actually bonds, fills the chips and scratches, and sprays a hard acrylic-urethane coating in even coats. It takes about a day. Your tile stays where it is, your plumbing is never opened, and you aren't living without a bathroom for a week. The cost is a fraction of a replacement, and most of that gap is the demolition and the plumber you didn't have to hire.
There are cases where it's the wrong answer, and an honest contractor will tell you so before taking your deposit. Rust that has eaten through a steel tub from the back cannot be coated over — the failure is structural and it will come back through the new finish. A fiberglass tub with a soft, flexing floor has lost its support underneath, and a coating won't stiffen it. And if the tub has already been refinished two or three times, each layer makes the next one less reliable.
The other reason to replace is simply that you want something different: a deeper soaking tub, a different footprint, or a walk-in shower where the tub is now. Reglazing makes what you have look new. It doesn't change what you have.
Aftercare is where most refinished tubs get ruined. Give the coating the full cure time your refinisher specifies before you use it. Then skip abrasive powders and anything with bleach in daily use — a non-abrasive cleaner and a soft cloth is all it needs. Treat it that way and the finish lasts; scrub it with a powder cleanser every week and you'll be calling someone again far sooner than you should.