To answer as best as possible given the vagueness:
Cookies: Highly compatible with most if not all browsers (and even headless tools). Lends themselves to having an expiry date and generally best when used with time sort of short-lived expiring session.
JWT: Everyone tends to use these in a stateless manner which means once issued, somewhat impossible to revoke without invalidating all JWTs or having a blacklist (and we're back at stateful). Plus some implementations had issues with downgrade attacks I think it was...
OAuth 1: Fine assuming you could keep clocks in sync and guarantee the secure storage of the keys/secrets. Good in that it didn't rely on HTTPS but if the secrets ever got compromised then the attacker would have free reign of that account until detected.
OAuth 2: Basically a complicated way to get short lived session tokens, potentially from a 3rd party API/auth source. Relies entirely on HTTPS to keep data secure in-transit and less of an issue if the session token gets compromised since its ideally short lived (because most want it to be stateless - those who keep a valid list of tokens sometimes skip the token expiry).
Cookies: Highly compatible with most if not all browsers (and even headless tools). Lends themselves to having an expiry date and generally best when used with time sort of short-lived expiring session.
JWT: Everyone tends to use these in a stateless manner which means once issued, somewhat impossible to revoke without invalidating all JWTs or having a blacklist (and we're back at stateful). Plus some implementations had issues with downgrade attacks I think it was...
OAuth 1: Fine assuming you could keep clocks in sync and guarantee the secure storage of the keys/secrets. Good in that it didn't rely on HTTPS but if the secrets ever got compromised then the attacker would have free reign of that account until detected.
OAuth 2: Basically a complicated way to get short lived session tokens, potentially from a 3rd party API/auth source. Relies entirely on HTTPS to keep data secure in-transit and less of an issue if the session token gets compromised since its ideally short lived (because most want it to be stateless - those who keep a valid list of tokens sometimes skip the token expiry).