What I've noticed in older capacitors and cheap eloctrolytic caps is that high frequencies in the tweeter can sound grainy, too much edge, too crisp and fatiguing on the ears or oppositely some people notice that the speaker sounds flatter, less fidelity than it used to, highs are no longer bright and revealing. It really depends on individual equipment and circumstances. You may not notice it consciously or you may if you are paying attention and know the speakers really well.
the better the quality of the speaker the better it will respond to upgrading the crossover.
what can be expected by a rebuild?
Balance to the crossover settings restored
Smoother sounding highs and mid range, bright in a revealing way, not harsh.
subjective: perceived warmth to the overall sound of the speaker if you upgrade the capacitors to poly caps
sound will hopefully be clearer and easier to focus on and hear detail within music
instruments should sound more realistic and full.
integration between the woofer and the tweeter should be as seemless as possible so that the sound appears to be coming from only one source, not two or three seperate drivers.
Most often it is only the capacitors within a simple crossover design that need to be replaced. This can greatly improve the performance of a speaker especially if it is over 20 years old.