What should I choose??

yes but its his choice. 

Changing the speakers will obviously make the bigger difference. Whether that difference is an improvement or not and worth the change, is up to you and your listening preferences. I agree with the other poster who advised you to ask your dealer to loan you the amps for a weekend.

Bryston and B&W would not be a good fit. You need an amp that would add warmth. For some time, B&W paired their speakers with Classe amps for just this reason. Mcintosh amps would also add warmth.

Hello, one issue is your amp is getting old. Most people in here knows that 20 years is the approximate life of an amp due to the caps. An option is new caps. Maybe even upgrading them to something better. Way cheaper and better sound. 
I agree about room treatment. It’s like owning a really nice sport car with cheep tires. It sounds like you have the means so start with the room treatment. 
After you have done those two things you can check out speakers. Maybe there is an option to upgrade the components of the speaker. New mids and diamond tweeter. 
This might add up to your current budget and improve the sound the most. 
Try upgrading to silver interconnects or speaker wire to get the detail you are craving with your old speakers and amp. Test first, it can get harsh with some systems. 
Last but not least. Test, test, test. 

I would save up and buy both at the same time.