Should I replace a front cracked Veneer with another Veneer or is a Crown okay?

I had half of an upper front veneer crack and break off. A Dentist was able to glue it back on but 4 years later it's showing a stain where the crack is. Insurance will pay for some of a Crown cost but not a Veneer.Is replacing a Veneer with a crown a bad idea or does it matter? I realize a crown will require more tooth to be removed and other dentists have told me they prefer to save as much tooth as possible. Thank you.