How big of a difference do amps make?

the source makes the most difference 'cuz if the source does not create the sound, the downstream components are sure not going to amplify them! so, i would 1st spend money on your source, get it to where you feel comfortable money-wise & sound-wise & then spend the money on pre & power. buying superb amps before having a source that can take advantage of it would be putting the cart before the horse. IMHO. FWIW.

Crucial.

I think they are every bit as important as speakers, the best speakers in the world just let you hear what your amp sounds like.
I'd rather have a $200 used pr of KEF standmounters with a 10K amp than other way around.

Contrary to Schubert, I drive my Aerial 10T with Sunfire SRA(bought NOS $450). Feels like I need a-bit more power of let's say Sunfire 300(used $700) and I'm sure that it will sound waywayway better than $200Kef with Halcro or Mark Levinson monos. At the same time I don't think that mine do well with 30wpc OTL tube amps or vintage Fisher receiver due to lack of power.

Without sufficient power to the specified load of the speaker neither price or sonic performance copmarison relevant.

Depends on the speakers. Some just can't make use of extra power. Matching amps to speakers is more important.

Cue Ralph's link to the "power paradigm"...