Can a change in capacitor alter the sound reproduced (either better or worse)?
It depends.
Like higher or lower values?
Again, it depends.
Example #1:
Input cap. Change it to lower values and depending on the input impedance, you also alter the low end frequency response. Change it to a too high a value and you end up with a lot of output offsets and what not.
Example #2:
PSU Supply Filter. Change it to a lower value and ripple will increase. Change it to a too high a value and the Law of Diminishing returns will kick you in the butt, seriously, there is no limit as to how much you want to use but it's all for nothing once you exceed a certain limit.
So in essence, it really depends on the function of the cap and where it is used in the circuit. This is where all the laughter comes from when you read someone changing a cap and says magical things about it without even understanding what the heck it's function is.
Example #3:
Ceramic capacitors. Any self respecting designer would not use a ceramic cap as a miller compensation cap or a feedback cap. You will read all sorts of bad things about ceramic caps from audiophiles and airbags but why in the world do those cap manufacturers still make them?
Because they are very good at filtering high frequency harmonics.
Now enter an audiophile airbag DIYer who sees those fugly ceramic caps and starts ordering online Wima and other film caps and readies his soldering iron. Geez I crack myself up.
Different brands with different performance?
Depends on the datasheet.