A difficult matchup for both sides as far as I can see, although I'd have to give it to CD overall.
For small ships, although the iCourier is a pretty solid fighter and is widely used in PvP because of its greater utility thanks to more weapon mounts, the Vulture is still very much the king of the heavy fighters thanks to its very strong distributor and oversized shield generator (even if the absolute shield value isn't much better, the Vulture has much better regen than the iCourier). The Vulture also benefits from larger individual hardpoints, so it isn't restricted to specific weapons in order to take down enemy hulls.
Medium ships again go to CD because of the effectiveness of the FGS coupled with FAS support. The Clipper is a solid ship, but it can't hull tank nearly as well as the CD mediums, as well as lacking in most respects other than outright speed compared to the FGS (FGS has both greater firepower and greater potential utility on hardpoints as well as having a SLF). Ultimately, all the medium pilots would have to be quite careful in such an engagement though, as they are relatively large targets but are not significantly tougher than the small ships; a fair amount of the outcome would rely on trying to keep the mediums alive so they can continue contributing (particularly FGSs, as they can support with their SLF from very long ranges even if the ship itself is in poor condition).
For the large ships, the Cutter is notably tougher than the Corvette while the firepower award goes to the Corvette. However, the degree of extra shielding afforded by the Cutter is greater than the firepower increase on the Corvette; if it turns into a matchup of distributor-limited facetanking then the Cutter would win simply due to its large shield capacity. Obviously, they wouldn't just facetank, but even in terms of ability to avoid fire they are not too dissimilar, with the Corvette having the greater maneuverability and ability to remain on target, while the Cutter has the speed to not get caught out and to escape tricky situations. Overall, I'd say that the Cutters have the Corvettes beat simply by virtue of being a bigger, tougher ship rather than any particular specialisation or quirk.
Ultimately, I see CD's heavier firepower, particularly in the small and medium categories, stripping away the small and medium Imperial ships quite effectively. Once it is basically just the Cutters left, their prodigious shielding would simply prolong the inevitable as they are left outnumbered by the Feds. Even if durability is important in a 1v1 matchup, in a team battle it just consigns a damage sponge to be ignored for the first half while struggling to contribute as the enemy forces leave them until last. The Feds, with their greater firepower and ability to stay on target, would be quite adept at killing off the Couriers and Clippers early in the battle.