It's funny, I don't think of Elixirs as bright. They sound pretty good to me, but the highs really feel hollow.
There are certainly brand-to-brand differences between strings, but I generally believe the following about roundwound strings:
Steel almost always sounds brighter than Nickel and stays that way longer. The coated steel I have tried has been a bit less bright than uncoated.
I prefer hex cores to round cores. I think round cores are probably more pure in the fundamental, but the hex cores help to bring out a warmer tone.
Thin strings sound thin. You can hear the difference between a set of 40-100 vs. 45-105.
In general, if you don't like DR High Beams, you'll probably like Lo Riders in the steel or nickel version (I do). I don't particularly like High Beams, and I didn't like the set of Black Beauties I just tried either. I would like to try the Bootzillas, though.
All that said, let's not forget our hosts. While I haven't tried them, I expect to like Alembic CX-3 strings when they eventually arrive on my new bass. The combination of the hex core and not-quite-round wrapping should be very pleasing.
-Bob