Jlove

Surprisingly, Alaska can feel quite different in May than July, or September. The state, however, isn't "frozen over" in May, if that's what you're thinking, and cruise ships will likely cover the same territory.
Some differences: Less rain (generally), mosquitoes and tourists in May. If going overland for a portion of your trip, maybe less "green" in May.
Tourist season generally opens after Memorial day. So prices and crowds increase after that. Fishing can also vary throughout the summer (eg., different salmon at different times).
Also, daylight is long in Alaska in summer, and can change by 6 minutes/day, depending on where you are, peaking over the solstice, June 22. So if long daylight is an issue (sleeping, etc.), then this is something else to consider.
Lastly, September - the other "shoulder" month, is also a nice month. More rain likely, less daylight, less tourists (post Labor day). "Indian summers", unpredictable of course, can be fantastic in early fall. And more likely to see northern lights with more nighttime.
Prices are sometimes lower, like on the state ferries (which take you to many of the same, and more, destinations as the cruise ships. Fall can feel more like winding down, calming relative to the rush of spring/early summer.