Levinson 432 VS. Bryston 4 BSST

Have you addressed room treatments? - That will make a larger STEP UP if you haven't
Are you running fully balanced Cabling?
Have you dropped in dedicated 20amp circuits?

All of these will make a bigger difference for less money...

If you like the Levinson sound, then the refinement of the Levinson over the BSST will show through and make a fine upgrade after these other tweaks have been accomplished.

While I must agree with Cytocycle about dedicated lines and room treatment, the jump (to me) from a Bryston 4 (a bright amp to my ears) to a ML 432 (I currently have the 433) is a major change, for the better to my ears. The Levinson is a smoother amp, and I personally think it is a huge step up from Bryston....

I just sat in on a demo of the Aerial 20T speakers. Source was the Levinson 390S powered by a Levinson 432 power amp ... I'm still shaking. It was absolutely breathtaking and the best setup I have heard in recent memory, maybe ever. I'm currently running a Levinson No.23.5 and No.27 in a bi-amp configuration, matched with a No.37/360S front end. I couldn’t even bring myself to consider making any change until I heard that setup. I will have to settle for Aerial model 9's and my current setup but that Levinson 432 was a peach. If I had the cash ... I might consider the upgrade. Granted they were $30,000 speakers but my more modest setup matched with Aerial 6's is very, very sweet in my opinion. I feel there is a synergy match between certain power amplifiers and speakers ... and I found a good combo. That being said you may want to seek out a company that is willing to let you demo at home OR buy a used 432 and live with it for 5-6 months. It might be the only way to know for sure. I see the 432's sell pretty fast.

PS .

I whole heartedly agree with Cytocycle; I have done the separate power runs and I have deadened my room as much as possible. It made a significant difference so if you have yet to do make those changes I would consider them first or in conjunction with the amp upgrade. What things do you feel you like/dislike about your current setup? what speakers are you running? Can you describe you listening room?

Thanks to all who responded...My room is a roughly 14 X 18 sun room...full windows on 3 sides...hardwood paneling...I have good interconnects from cardas high quality (not insane) speaker runs..(the speaker cables are longish 40') and have to be that way because of the space...I know windows can be problematic but thats the space available...My speakers are the Tyler Acoustics Linbrook Sigs....very happy with them..My pref. in sound is full big bass....with tight high end with plenty of contrast without rolling off...The speakers I used to run were B & w's which had a big sound but too bright....If any thing that I could bitch about is a lack of warmth...not sure if that is the right word....Not really unhappy with current setup...Haven't hit that..."This is it" plateau....thanks......

Consider a 334. Very nice amp. I have Tylers also and love them. Owned several Levinsons and had a 334 in my system on loan. Liked it much better than the 27.5 or 331.

I also borrowed a friends 4BST and did not like it at all. To much energy for me. Have not heard the SST.

Cytocyle is right on. No point of spending money on the amp until your room is treated. Consider the fact that in an untreated room, the difference between the 2 amplifiers may not even worth 2% of the price difference. If I were you, I'd consider something to treat the room first. Check out 8th nerve line of room treatments. They make the panels that are more or less WAF-friendly, not bulky and pretty affordable and functional.
BTW, you may get some warmth when the room's treated...you'll hear deeper into the music and it won't sound as bright.

I have an all Levinson front end-320S,36/37 and I love them.
You may also want to consider an amp like the Pass X350.
They go for similar money used,and you will not have any of the dependability issues you may have with the Levinson.Levinson doesn't even do their own repairs,they refer you to an independent repair facility.Good luck with that!!!
If you call Pass,you may even get to talk to Nelson himself,or hear him answer a question that you just asked the person on the phone.

I use a combo Pass Levinson system.

Pass is great company and the newest amps are world-beaters, but the 432 is very good.

I really don't think you can beat the Bryston also.

All good choices, if I had unlimited funds I'd get the latest production Pass amps.