I can't tell you about campaign map bonuses, but for units, the biggest differences are probably between line infantry. Sweden, Spain, Poland-Lithuania, the United Provinces and the US all share a "basic" unit. The Russians exchange accuracy and reloading skills for melee skills and a lower cost, the Austrians get larger, worse units, the British and Prussians have faster reloading, more expensive units that are better at melee defense and charge bonus respectively, and the French have units that are better in melee. Other than that, Sweden tends to have larger, more expensive cavalry, Austria has just better (but much more expensive) Cuirassiers, and Prussia has very slightly cheaper pikes. Artillery seems to be consistent across all European factions. Light infantry is identical for all factions save the Austrians, who replace it with jaegers, which are better. Grenadiers also change: Spain has cheaper ones, Russia cheaper, less accurate ones with superior melee stats, Prussia just better units (that are also cheaper than usual), and everyone else gets lumped with the same.
In terns of uniques, then Britain has loads, mostly better line infantry, most factions have at least one unit of elite line infantry a la Maison du Roi, Austria has light infantry coming out of its earholes (okay, like two, but still), and there are several elite cavalry units, such as two "Garde de Corps"'s (one French, the other Prussian), the Polish Winged Lancers, and the cheaper, medium-quality Haakepelitta (Sweden) .
Oh, and the Ottomans? Terrible, awful infantry until late game (when they get just about OK copies of European units) and good artillery and passable cav. The Indians get better inf and elephants.
I've probably missed out loads, so here is a link to a complete list of units. http://wiki.totalwar.com/index.php?title=Category:Empire:_Total_War_Units
