power differences in different bands on same radio?

Because the radios with the FM mode are not true CB radios. They're export radios. And they are not certified for used by the FCC.

A true CB radio has either 23 channels (if it was made before 1977) or 40 channels (if it were made 1977 and onwards). A true CB radio is only allowed to produce 4 watts output power on AM and 12 watts PEP on SSB. SSB is just a mode of operation on an AM CB radio, but it is a legal mode of operation.

The export radios on the other hand, are not legally certified for use by the FCC, because they produce more than 4 watts of power, or they allow you to operate it in the FM mode, or (in most cases) there's a "band" switch on the radio that actually allows you access to the "license required" 10 meter amateur band. (a.k.a. "ham") As posted to use the radio/frequencies, a license is required; if you are caught on those frequencies by a ham (and they do monitor them for intruders) they will track you down and turn you in to the FCC, who will send you a nice warning letter in the mail, with a nice hefty fine for repeat occurrences.

Unfortunately there is no way to make it the same across the board; at one time all anyone had was 4 watt CB's. Now everyone has a CB that puts out more than the other guy and "squashing ducks with little radios" has been a common occurrence since then.

 

The technical reason is the circuits in your radio are designed to work on a specific Freq and mode. The way it works is different in each mode. For instance AM VS SSB AM is amplitude modulation and uses a carrier and then modulation to excite that carrier to get a signal out. A SSB signal has the carrier suppressed down 40 DB or greater therefore no carrier is actually seen and the final will put out a little more wattage. In a FM signal it is totally different it uses Freq modulation. This all being said there are some of the CB Butchers as i call them that can strap voltage over to the Final and make the AM work as strong as the side band but you give up a clean SSB signal. I hope this helps you.