All three companies make very nice equipment. A lot depends on your surrounding equipment. For example, if you are interested in new amps, then it would be important to know what the pre-amp and speakers are. System integration is important and the ability to drive difficult speakers makes amp selection very detailed and important.
Unless you are going to remove all of your existing equipment at one time and replace them all together, then you are typically going to replace one piece at a time. This makes it important to demonstrate that particular piece in your system. Reputable dealers will allow in-home demonstration of equipment. This way you can do A/B comparisons vs the original piece in your system in your home. Listening to a piece in the dealer's show room isn't quite the same and many are very disappointed when they purchase and take it home without hearing it first in their own system.
I've heard many Mark Levinson and Audio Research equipment. I've never heard Bryston (that I can remember).
Much depends also on your price point and your existing system.
You didn't list your price point or your existing system, so you are going to get many responses that are biased based on particular preferences.
Are you keeping your existing speakers? if so, what are they? are you replacing pre-amp and amp and CD transport or just one? See? many choices and questions that have to be answered before a more specific response can be provided.
enjoy
