Singlespeed & Fixed Gear - Upgrading advice

I've got a Bianchi Pista with surly stainless steel drivetrain and phil/wood open sport wheels and was thinking about upgrading the frame to a Dodici Gara aluminum with carbon fork. Do you think ride quality will be that much different? Or should I keep the steel pista and invest my money into headset, bb, new carbon fork, paintjob etc. I'd be getting a new headset and bb for the gara anyway... Please let me know what you think.

It would help to know what criteria you're looking for in your upgrade, i.e. define "ride quality." Why are you unhappy with your current setup and components? Do you feel the Bianchi rides too harsh? Or is it an aesthetic thing (totally fine)?

Personally, I wouldn't spend a lot of money on a steel Pista any more than I would on something like a Kilo TT. IDK anything about the Dodici Gara, but it appears to be in the same league as a Vigorelli or Super Pista, both very good track framesets. And yes, I would expect a significant difference in ride and performance between the Pista and the Gara.

Regarding ride quality:

You'd be amazed as to what a nice set of tires will do to improve how a bike (or car for that matter) feels. Continental Grand Prix 4000 (AKA: GP4000) are some of my personal favorites.

If you're not sure about whether or not you should buy a frame, don't. If this is a street bike, I'd say don't upgrade anything.