On my wife's 4-wheel carriage one front wheel is noticeably tighter than the other, On a car I'd clean & re-pack the bearing, turn the nut down to tight then back off to line up the castle nut with the hole & lock it in place with a cotter key.
FWIW the metal wheels on her carriage look like they are the same those on a techie wheel-chair, though the tire is thicker.
What's inside the hub? Same as an auto wheel? And do I bother or just leave it be?
Chuck, what you suggested is what I would suggest too, for getting the wheel working better. Depending on your vehicle, the wrench to get the hub off is your first difficulty. Does the hub have a couple holes instead of a hex-headed cap? The European vehicles seem to take a special wrench with prongs to make the latches release for access to the nuts and bearings. Don't try prying it off, you will wreck the latches so the wheel isn't watertight anymore. Maybe you got a wrench with the vehicle, so no problem.
Husband said the modern metal wheels have two bearing sets, one outside and one inside of the hub, so both sets need need to be cleaned and regreased when you clean each wheel. Same two sets of bearings with the modern roller bearing wheels, that are made of wood on new carts and carriages. Modern wheels usually need cleaning and regreasing about once a year, unless you drive on lots of sand or cross water often, to get them into the grease.