One of the biggest differences I can see is in the damage system. Each ship has a few hit points, (small ships maybe 3, large ships maybe 8) but each has a level of armor...if you score 4 hits on an escort, you may have exceeded the damage value and caused a hit point of damage. But, it may not be enough to cause a critical (which typically do 2 hit points as well as some special damage). But, 4 points usually isn't enough to cause any damage to a battleship, and so the damage is ignored completely.
There are shields (which defend against regular guns) and point defense (which defend against torpedoes and small craft). These defenses never degrade (unless a critical knocks them down). Point defense has a 4" radius of effectiveness as well (escorts in close proximity can use their PD to defend the big ship against torps, for example).
Ships in squadron can combine fire to get through the armor. Big ships though typically cannot squadron. Fire arcs can be turrets, 90deg. fore/stbd/port/aft, or fixed fire arcs (boresights). Some ships can leave mines in their wake that will attack enemy ships.
Weapon systems have 4 range bands, each 8" distance. So most weapons can shoot out to 32" in distance. The effectiveness varies by type. Torpedoes are typically more effective against farther targets. broadsides are typically more effective at range band 2 (8"-16").
Some ships have stealth that makes them harder to hit (higher target numbers), but they also lose some weapon effectiveness when using it (fewer attack dice to broadsides, but not torps).
rolling dice is typically 1-3 no effect, 4-5 1 effect, 6 is 2 effect and can be rolled again (like beams). So if you roll 12 dice, on average, you'll get 1,1,2,2,3,3,4,4,5,5,6,6...for a total of 8 hits, with 2 dice you get to roll again and add to the total. I've seen some crazy number come in by rolling a series of 6's. (like a 4 die mine that did 22 hits!)
As the previous poster said, the fighter combat is a little comlex (you have fighters, bombers, interceptors, and assaulters) and they all have interaction between ships point defense and other attack craft. But with a few games I think that will be less of a worry.
I'll be bringing my terran fleet to kublacon 2010, and hope there's some games going on.
Chern