This may sound dumb, but I always figured that since there were only two people (or maybe just a few more) using the Dark Side through Sith teachings that somehow there was a greater store of power that was more easily accessible, as opposed to there being thousands of Jedi all drawing on the Light Side in the same way.

This kind of makes sense if you consider that:
1) In old republic times, there were thousands of Sith and Jedi who seemed rather equal... I know you mentioned the trailers but you have to admit that the Jedi hold their own in the trailers and the Sith usually seem to win because of better lightsaber fighting than force use.

2) In the prequels, only the more advanced apprentice (Dooku) can use force lightening... it doesn't seem like Darth Maul has any advanced force powers and is just really handy with a lightsaber.

3) In the original trilogy, when there are a lot less Jedi in the galaxy, Luke (a barely trained padawan) fights a full-blown Sith Lord for quite a while, though he eventually gets pwnd and loses a hand. He comes back better than ever just a few months later (and, notably, after the death of the last Jedi master) and is able to defeat Vader completely.

4) If you consider that, in the movies, the Jedi pretty much apprentice anyone with Force talent whereas the Sith only apprentice (in most cases) Jedi knights/masters who have shown a remarkable ability with both the Force and lightsaber skills, then I figure it makes some kind of sense.

I think the Sith are just more discriminate in their recruiting. They only take the best of the best as apprentices, and as such are usually able to outclass their Jedi opponents.

Just my opinion, though.