The Ulysses is my personal favorite fighter and in the hands of one who can appreciate the high maneuverability, it more than makes up for the low missile capacity.
I'll second the comments about its handling. It turns extremely well, moves pretty quick, and it's tough to hit. An adept pilot can become well schooled in ways to avoid presenting the ship's broad top silhouette, forcing chasers to try for hits on the narrow side and rear profiles. The small secondary bank limits the realistic ability of this craft to wade through a wing or two of enemy ships quickly, but as a dueling and harassing fighter it's near the top of its class.
I always wanted to love the Ulysses, but in the end it was never quite up to my standards of durability. Fun to fly and ideal for a 1v1 turning fight, but it can't induce the same kind of show-stopping, Shivan-leveling pyrotechnics that a Hercules or even an Apollo can. Keep that in mind before trying to wade through a wing of enemy fighters on your own in an Ulysses. It makes a superb dogfighter, however, and is serviceable for any mission where enemy fighters will be your primary targets; bomber escort and protection of friendly craft against which a bomber wing would be overkill are ideal posistions for the Ulysses. True interceptor duties are problematic due to a small ordnance load.
The best thing to note about the Ulysses is that it is virtually the only fighter you have access to that can actually match the maneuverability of an SF Dragon. However, secondaries are small, and it isn't compatible with the most powerful of dogfighting cannon, the GTW UD-8 Kayser. It also maneuvers a bit too well, because people unfamiliar with its handling may find themselves overshooting.
The Ulysses has 180 more shield points (almost twice as much) than the Serapis, although a slightly weaker hull. The Serapis also has nearly twice the secondary capacity, while otherwise weapons compatibility is pretty equal, with both fighters supporting Maxim and neither supporting the Trebuchet or heavy weapons. A comparison between the Ulysses and the light fighters of other races is what you'd expect. Like all Terran ships, the Ulysses has stronger shields than its Vasudan counterpart while being a bit slower.
The Ulysses is on par with the Valkyrie. It has a smaller target profile which compensates for the Valkyrie's larger target profile and heavier hull. Its primary guns are better positioned, which compensates for the Valkyrie's superior secondary capacity. The Ulysses is more maneuverable, but the Valkyrie can outrun anything. To ravage through endless waves of hostile fighters with your primary weapons, I suggest the Ulysses. The Valkyrie can, however, do more damage to cruisers if it's furious enough.
Fitting this craft with a Morning Star/Flail, Maxim, or other rapid-fire weapon makes it an excellent bomb interceptor, but by FS2, it's a rather outdated design not really as effective as before. It has a large shape if attacked from the top, plus the Kayser isn't usable as said above. However, if you're an escorting scenario, then use it. It's what you need to distract the enemy.
The Ulysses is a a good enough fighter in FS1, but very specialized--it is good for a dogfight and little else. In FS2 it is completely outclassed by the GTF Perseus
which fulfills its role as a dogfighter but has the payload to be an effective interceptor with the GTM Trebuchet
and the durability to carry out light strike missions.