Input impedance is (one of) the big elephant(s) in the room when it comes to preamps. How the input stage loads the source has a big impact on how it sounds and some sources are more affected by loading than others so some sources will sound almost identical with two different preamps while others might sound very different. Output impedance also plays a role as the preamp will be loaded (or not) by whatever it's signal is feeding.
There's more to good 
gain-staging than just gain, and the subtleties of impedance matching 
are seldom explored nowadays.  Back when engineers wore white lab coats 
(and, in many cases, were actually engineers), a lot more thought
 was put into that sort of thing.  Through impedance matching or 
deliberate mis-matching, a lot can be done with how a preamp sounds that
 all sits outside of any "baked in" sound a preamp might have.  
That
 "baked in" or "native" or "default" sound that certain preamps have, 
combined with how stages are gained, further combined with how input and
 output impedances are taken into account are the triumvirate, and the 
first item on the list is often the only one that people consider.  It's
 one of the drawbacks of the recording renaissance we're living in; 
anyone can do this at home now and they have access to great gear for 
cheap and it's easier than ever to get good results, but they still have
 to know what they're doing to get better than good results.  Really 
understanding how things work is worth more to the "accumulation of 
subtleties" than how a preamp sounds.  That preamp sounds different 
depending upon how one uses it.  Most people recording at home don't 
understand any of that and even fewer have any inclination to learn 
about it.
My response to Ethan's response:
Yes. The input impedance is a thing. But most 
microphones don't get that much out of changing the input impedance. 
Oddly the ART preamp does indeed allow one to change the impedance. I 
play with it sometimes. It doesn't really do that much for me. 
These
 days output impedance is virtually moot. All inputs are high impedance.
 I wonder how, say, Scully and Ampex machines used to be in the early 
and then the late 60's?
 





