I generally set my crossover materials to be around the time of the Enterprise-B and used mostly TMP-TUC era stuff. I keep the phasers and turboslasers as basically equal. Federation style shields are slightly better, but only so their small size doesn't get them destroyed by a hail of fire from an Imperial starship.. I do have photon torpedoes as being quite powerful, but most Federation style ships can't pump them out like there is no tomorrow (especially when they are generally outnumbered.
I do not set the crossovers in the Milky Way. I always set them in the Star Wars galaxy. Arriving two years before Yavin. Warp drives are quite slow compared to hyperdrives, but I can also imagine the Rebel Alliance acquiring some smaller or older hyperdrives for the Starfleet engineers to install into the Impulse decks to at least somewhat correct that problem. Using the warp drive in hyperspace to reduce the time to roughly the speeds the Empire uses.
If Starfleet style ships ever seem overpowered, it usually doesn't get them much but the ability to escape, or complete an objective, because they are still outnumbered and require aid and/or time to establish bases, supply lines, and ways to repair and resupply their ships, since this would be early replicator or proto-replicator days at best, if at all. Plus they would have to work through the Rebels to keep their starbases hidden from the Empire until better defenses can be setup.
My setup was also never the Federation exactly. I tended to have them be the faction of Starfleet that was opposed to the treaty with the Klingons (but for more noble reasons, since I was using FASA materials at that time.) They rebelled to protect the Triangle from the Klingons and Romulans because the Federation wouldn't due to treaties. After several years, they lost, but found a means to evacuate the region and resettle far, far away....only to come into another civil war. I had the Federation later come to a agreement with them to cover up this dark period, which ends around the time Picard is born and the aftermath and evacuation is covered up with the Tomed Incident. (I did this while on the boring walk to and from school from seventh grade to my senior year of high school, which was now over 20 years ago).