Short answer -
winter.
Hurricane season is basically the same in both oceans. Leave
Florida November/December. Transit
canal anytime January-March. Want to leave
Panama for
Hawaii before the monsoon season changes, usually sometime in April. Once that changes the winds will be light for a long way off the coast. Otherwise the whole trip is a
classic tradewind
passage, with a little bit of
work getting clear of Florida (depending on which
route you select).
The
passage from
Panama to
Hawaii is a long one - 4000+ miles. We did it last April non-stop. If you want you can coast up
Central America and shorten the big hop somewhat, although still best to be out of
Mexico by May so as to arrive by early June before Mexican
hurricane season develops.
Hawaii does not
traditionally get early season hurricanes, but YMMV.
That's the short version, check Cornell (
World Cruising Routes) for a few more details.