Is galvanized steel wire better for fences then non-galvanized steel wire?

There's really no such thing as a steel wire fence without galvanising. An ungalvanized steel wire fence would rust the first time it rained. Therefore you'd rather have galvanized steel or another option.

Yes, galvanized steel wire is better suited for fences instead of non-galvanized steel wire. The reason for this is that the galvanizationn process coats the steel with a zinc coating, making it rust-resistant in the presence of moisture.