Best all-around: X-wing
Otherwise they're purpose-designed craft, so really impossible to compare outside of that.
The TIE is fast and highly maneuverable, but has weak, single purpose weapons and no effective defensive armament to speak of. Like a Japanese Zero without the bombs. Its purpose is as an attack craft against small or lightly defended targets, with the military advantage largely based on fielding significant numbers.
The TIE Interceptor is even faster and more maneuverable, and has more firepower, but suffers from similar defensive weakness. Again, it's an attack or intercept craft against light targets.
TIE Advanced (Vader's craft) is more versatile, equivalent to the X-wing, with a general role as a heavy fighter capable of prolonged combat against heavier targets and light space-to-surface missile runs.
TIE Bomber is what it says it is; a light bomber intended for significant targets, though not necessarily heavily defended ones. A Stuka comes to mind, perhaps?
As for the Rebels, the Y-Wing is roughly equivalent in intent to a Mosquito fighter-bomber. Not fast or particularly maneuverable, but well armed and with significant defensive protection, it's a flying tank, intended for heavy strikes against large, well defended targets, but not for dogfighting (though it can hold its own).
The A-wing has real zip, matched only in speed and maneuverability by the TIE Interceptor. Though its primary weapons are weaker, it can field guided missiles and has defensive capabilities that the various TIE models lack. An excellent dogfight craft, with a clear role as such, like a Spitfire.
The B-wing fits the category known as a "strike interceptor." Neither significantly fast or maneuverable, it nevertheless outclasses the Y-wing in these areas, and carries heavy weapons and defensive armament second to no other "fighter" vessel. Again, not intended for dogfights, the B-wing's role is primarily to attack heavily defended targets, including small capital ships (as a squadron, of course, not one-on-one). Think F-111.
Outside of the films there are other craft, but these are the core you seem to be thinking of.
