I would look to the preamp as the source of the brightness. Check out other brands such as the Art Audio VPL you will be much happier.
In response to your question, I've never known bryston to be known for brightness. However Thiel's on the other hand are known to be bright particularly in certain applications.
Having said that, ARC equipment mates well with each other, so from that perspective the 150.2 would definitely make for a better combination.
I'm saying that also because I have the 150.2 and have had the LS-2 mkII and brightness was not an issue with either of course I had different speakers and components.
It is not the speakers. They measure pretty flat and much much flatter than a lot of speakers out there. I don't know anything about ARC 150.2 but what price range are you in?
For what it is worth I listened to the 2.4 and 3.7 a few weeks ago with Musical Fidelity A5 integrated and it sounded very good. It was very neutral. It was warm when the recording was warm and bright when the recording was bright. I find Thiel more detailed than most other speakers.... I think people tend to think they are bright because of it. It could also be that people were not give the older Thiels the power they needed to sing.