There are different scales used for other guitars but for sake of simple example, I will only relate to the two aforementioned scale lengths. Nevertheless, the tones will be different on ALL scales as you will see later in this article.
It doesn't matter if you have single coil pickups on your Les Paul (24.75) or Humbuckers on your strat (25.5). It's not the pickups! It's the scale or rather the point where the string is suspended which is at the nut and then the bridge. See, in order for your guitar to be tuned to any given frequency, a precise amount of tension much be placed on the strings. The longer the distance between the suspension points = the greater the amount of tension. How does this effect tone? After all, we all know tone is in our fingers and our techniques! Well, you are right! HOLD ON, you are going to play a little differently if you have to push harder, snap it more or exert more force. Well, you still don't believe me??????
The harmonic overtone has evenly spaced nodes along the string doesn't move from it's resting position. This is a fact. However, if you are to place the nodes on a map where you compare the harmonic overtones (which contribute to the timbre) of a 24.75 inch guitar vs a 25.5 inch scale guitar, you will find that the nodes are not similarly placed. The harmonic overtones on a 25.5 inch guitar will have wider spacing while the 24.75 will have a narrower spacing. This spacing if long (25.5) will produce a E note with brighter chime and shiver (a little esoteric but bare with me) while the narrow tighter pack harmonics of the short scale 24.75 will have a thicker, warmer E sounding tone.
But wait, Jimi Hendrix, Stevie Ray Vaughan, Eddie Van Halen, tuned to E flat and especially Eddie - He had monster tone! Yeah, EVH called it the Brown Sound. It's world famous!! But still, this is a compromise. You can get close to a Les Paul sound by de-tuning your long scale (25.5) guitar. You can put heavy gauge strings on the Les Paul to increase the string tension but the fact remains - the scale is a fixed point. You could build a guitar that has a moving nut but the distance between the frets will be off. Regardless, if you had the all the lab equipment at MIT you would never be able to find the exact same mathematically, sonic-ally specific tones on guitars of different scale.
I have heard the same old minutia about "it all in the hands," yeah I know buster! But it's also like this:
EAR > BRAIN > HAND > PAPER = MUSIC
BRAIN > HAND > INSTRUMENT = MUSIC
When the hand is deployed it has input to the brain. Different string scale effects the elasticity and tension of the string (to say the least). Therefore, your guitar scale effects your tone in a large way. One scale is not better than the other. Both are brilliant!! By all means, experiment and HAVE FUN with your guitar, bass, and I hope you now are more informed!