what impacts the sound quality more amp or pre-amp

my system is

B&K ST202 (I think its a sonata series??)
B&K 10ProMC
Alon II speakers
Jolida 100 cd

Are you sure that you want to rule out an integrated?
Personaly, I don't consider separates unless I am prepared to spend thousands, at least couple of them.

The Alon II speakers are specified as 87 db efficient and are, I think, 4 ohm nominal impedance. This is a difficult load for most tube amplifiers to drive.

My personal feeling is that if you want tube sound that you should go with a tube amplifier. I think this makes the most difference. But it implies certain speaker choices too.

From a practical point of view, it is going to be challenging to find a tube amplifier for $500 - $800 which will be able to reasonably drive your speakers.

In the context of your system and with your budget, my feeling is that a tube preamp would be your best bet.

The Mapletree Audio Line 2A SE preamp is $760 new. It will likely survive many system changes and upgrades that may or may not be in your future.

"The Alon II speakers are specified as 87 db efficient and are, I think, 4 ohm nominal impedance. This is a difficult load for most tube amplifiers to drive."
No mention is made of phase. This would be the deal breaker for tubes, that and wide swings in impedance.

4ohm and 87db are nice, but not deal breakers for tubes. Harbeth, less sensitive and considered tube friendly.

Tube amp choice, however, DOES imply certain speaker choice.

pre is the heart of the system. As said balancing it all out helps more.