They are going to sound different because they are different. High fingers typically sound more staccato like, more clear, more defined. You typically hear Mozart played a lot like this. Low fingers is going to sound more legato, more "romantic", more "cantabile".
Even though terms like legato and staccato may at first seem binary they are not. You can have extreme legato that is effectively like holding the pedal down. It's usually expressed notational through ties but usually only certain types of figures work well for this(arpeggios). You can have very slight arpeggio that barely connects notes. High fingers help produce that since one will have to spend more time with the finger being lifted and so it will cut down the sustain it would normally have with close fingers. That is, by focusing lifting the fingers higher one naturally is going to have a "shorter legato". Note though that the instrument can mess with these to a degree. It's possible "high finger legato" was developed as an awareness by concert pianists being in environments where there was too much reverb and they felt their fast scales sounded too harmonically blurred from what they were used to hearing in and figured out that they needed to reduce the legato. Even going so far as playing legato as some degree of staccato if necessary. Likely it was something that developed subconsciously over time with some people playing it high and others low due to how they practiced and it producing a certain type of sound which some music seems to prefer because it produces a more musical effect(clearer, more harmonious, etc).
The main thing is that it's just a different quality of sound. Just like dynamics. Do you want to be stuck with only one(or two, or just three) way of having to do things?
Like all things, one wants to have control/options.
Topic: High finger legato vs close finger legato