The quick answer to the question is that in any given strain the seedless females (ie "sinsemilla") will be much more potent than seeded ones. So the best quality weed is always seedless, and if you have the ability to create seedless weed, you ought to do so.
In general, the only way to absolutely ensure seedless weed is to grow it indoors. Outdoors, female plants are at the mercy of stray male pollen that can float for miles through the air. If someone half a mile away from you didn't pull all their male plants, your outdoor female could get fertilized.
Next, the seeds take up a considerable amount of weight all by themselves. If you're paying per pound for weed, of course all else being equal, you want seedless. Lastly, seeded weed requires more work to prepare for smoking. Wouldn't be a big deal if it were stronger, but since its weaker in potency, that's just another negative.
Does the male strain matter? Of course it does.
If you cross a male chihuahua with a German Shephard female, you don't end up with a German Shephard. . .you end up with some sort of mix. The same is true of pretty much **ALL* sexual reproduction. The offspring will exhibit traits from both parents.
Now genetics is a bit complicated, more than I'm willing to go into in a short post like this, but if you were to cross White Rhino with Bubblelicious, yes, you'd end up with something different than either White Rhino OR Bubblicious. You might end up with something that had positive traits from both. . .but you might also end up with something that had negative traits from both! (Or some positive, some negative, etc).
Not only that, but if you did that cross ten times, in theory you might end up with ten different offspring each with slightly or even vastly different characteristics (ie "phenotypes").
This is the same way that siblings from the same parents will look a little different (in some cases dramatically different) and have their own unique personalities.
Much of the art of breeding (weed, but anything else, including tomatoes, dogs, horses, etc) is recognizing which phenotypes are desirable, then cross, or back-breeding them to stabilize their genes into a true-breeding strain.