Both veneers and crowns cover a tooth to change how it looks or to protect it. They differ in how much of the tooth is removed and in what they can repair, and that difference is the starting point for choosing.
What a veneer is
A thin shell bonded to the front of a tooth. It usually needs a small amount of enamel to be removed, and the change is permanent. It is mainly cosmetic and suits healthy teeth that are discoloured, chipped, worn or shaped in a way you want to change.
What a crown is
A cap that covers the whole tooth. It needs more of the tooth to be shaped, but it protects a tooth that is weak, cracked, heavily filled or has had root canal treatment. It can also sit over an implant.
Which problems each one solves
Veneers address appearance on healthy front teeth. Crowns address strength. If a tooth is structurally weak, a veneer will not protect it. If a tooth is healthy and only the colour is the issue, a crown removes more tooth than needed.
Alternatives to consider first
Whitening can change colour without removing tooth. Bonding can repair a chip or close a small gap, with little or no tooth removal. Ask whether these could achieve what you want.
Lifespan
Both usually need replacing at some point, so cosmetic work is an ongoing commitment. Ask what the replacement would involve and what it costs. Grinding or clenching teeth shortens the life of either and a night guard may be advised.
The short version
Choose the least invasive option that solves your problem, and be sure you understand that shaping a tooth cannot be undone.
General information, not medical advice. A qualified dentist decides what suits you after examining you.