Don't you hate when someone asks a question here and then abandons the thread? No questions answered, and never a follow up?
@delandz has asked 7 questions over the last 13 years and never replied after or followed up. He's also never replied to a thread.
Anyway, my answer to this odd question is as follows. And by odd, I mean he never states why he needs to replace the breaker, or why he needs to know the wire size. Was it all ripped out, or something?
Most boats that I am familiar with, including my Catalina 36 and Tartan 3800, have a single AC outlet circuit. The breaker is to protect the circuit wire. A choice must be made: do you want a 20 Amp circuit, or a 15 Amp circuit? For the 15A circuit the wire is 14 AWG. Most boats I've worked on just used household, solid conductor Romex, 14/2 plus ground, or 12/2 plus ground. You really should use marine-grade stranded wire, with green, white, and black insulated individual wires in a white jacket. It's more money, but it's the proper way to go, since wiring on boats will flex more than in houses, and the flexing could cause work hardening and subsequent breakage of solid conductors. I've never seen that happen, but there you go.
Once you've decided on a circuit current, you get a matching breaker, and matching devices. The very first device in the circuit from the breaker should be a GFCI device. This device can then feed all of the other devices, and the entire circuit will be GFCI protected. This is important on a boat. Don't "star wire" from the breaker, run everything in a single line from the breaker, through the GFCI device.
I think a 15A circuit will almost always suffice. In rare cases folks might want to run 20A loads, but I honestly can't imagine what and why on a boat like this. 14AWG marine triplex is about a buck a foot, 20AWG about $1.75/foot. Devices and breaker are about the same, maybe marginally more for 20A. (By the way, I just checked Amazon for the marine wire, and Home Depot for the household, and the marine is cheaper!!!)
I hope this answers the OP's, and others' questions about this. I am not an expert, and have not consulted the ABYC standards or anything else on this, so don't go by me, do your own research, too, and/or hire a professional marine electrician.
To the OP, as others have suggested, read the writing on the old breaker, read the writing on the jacket of the wire. If all else fails, measure the diameter of the conductor: if it's solid, 12AWG is 0.0808" in diameter, 14AWG is 0.0641".