There is really no advantage one side to the other just for the sake of port or starboard. Figure out what directions you will be sailing in, and then figure out whether you like sunrises or sunsets. That might be one reason to pick a side.
Figure out if your cruise will be doing any shoreline cruising ie. in a southbound
Alaska cruise, you might see more on the port side.
My wife swears she prefers port side cabins, but can never articulate why when I ask her. You could get a balconey on the stern and not worry about which side.
Whichever side, make sure you're not above/below the casino or one of the bars or the theater. We seem to always reserve a cabin on the port side. Probably just because we've been on the port side enough times we're just used to it.
There are only two instances where I would choose one side over the other ... an Alaska Inside Passge cruise and a Panama Canal transit.
For Alaska, starboard heading north, port heading south.
There are no guarantees on which lock set you'll be in for the canal, but most people's experience (we've done it twice) indicates that cruise ships are usually in the "lower" lock set. That would be the right-hand set going to Florida, the left-hand set coming from Floria (or that direction, anyway). Going to Florida, portside, coming from Florida, starboard so you can see the concentration of action in the area between the lock sets.
Other than that, I don't see much difference. It's usually up to the HarborMaster which way a ship "parks" in port so it's impossible to predice whether your balcony will be ocean view or people view.