The body/neck makes more of a difference when you have a big enough amp & speakers and it's cranked enough for the body to vibrate in response to the ambient SPL.
Sometimes it can be a nearby bass amp from your bass player more than the notes you are playing yourself.
It also depends on how far you stand in front of the amp and if that is located in somewhat of a reinforcing node or cancelling node within the sound field.
When you're loud enough for a single string to have about infinite sustain, one or more unmuted strings often respond to the sound field and "play themselves" which is something to pay attention to. This is much more prominent when facing the amp which may or may not be done in a reinforcing or cancelling node, all of this are forms of acoustic feedback where "cancelling" does not mean stopping the feedback just making it sound different.
Your own body can block the sound a lot, and it can make a difference how much of the guitar body is exposed to the sound field rather than obscured.
Then there is magnetic feedback, with a high-power tube amp the large audio output transformer, which operates at high voltage and steps down the output to the speakers, can throw magnetic flux for a foot or more depending on orientation also. More so when you have exceeded it's linear performance specification. This flux will be modulated at the audio frequencies you are playing at the time and can go right into magnetic pickups non-acoustically. This is the other big transformer besides the power transformer, which is not found on solid-state amps which operate with only a single power transformer, no output transformer needed for them.
Strings, pickups, pickup height, position along the string, and speakers plus cabinet seem to make the most difference anyway. For instance on a standard Les Paul the adjustable polepieces are located directly where the 24th fret would be, this was also the traditional location on an SG up until about 20 years ago. Before that the occasional 24-fret SG's had only a bridge pickup. With the rise in popularity of 24-fret guitars, "all" SG's bodies have since been routed to accept a 24-fret neck even if it's only a regular 22-fret model, that's why there's a little plastic cover over the gap. Regardless, this way the neck pickup has not been in the same position as originally designed for quite some time.
It's only logical for the input transducers (strings/pickups/pots/caps) and output transducers (speakers/cab) to be the most influential, coincidentally this is where the most variation is commonly found, and perfection is furthest from being achieved.
Adjustable pole pieces are a worthwhile variable, remember these are Hall-effect sensors and along with overall pickup height are one of the only transducer variables to work with unless you change strings, pickups or speakers.
On single-coil pickups sometimes different length polepieces are wound in to begin with, and not considered to be adjustable. These are magnets themselves rather than screw taps into a hidden bar magnet. Technicians sometimes will push them up or down a little bit anyway to noticeable effect, depends on the pickup and overall good fortune because some of the hair-thin inner coil wires can be damaged if there is too much cementing depending on construction.
Strings are so important, the heavier the string, the beefier the signal. Stevie Ray Vaughan was known for his strong tone and one of the elements was heavier strings than average electric players use. Van Halen used light strings and his legendary tone was more dependent on particular electronics and the way they brought the weaker incoming signal up by comparison. Different technique made the playing characteristically different, different gear then made the tones characteristically different.
One of the good things to do is set up one electric and one acoustic guitar having duplicate scale length, string gauge, neck dimensions, action & intonation. IOW set the acoustic to be as good as it can get with no buzzing or anything wrong, where nobody who tries it can find anything to complain about. Adjust the electric to match. Naturally truly wimpy strings will not be acceptable, they do not have to actually be "heavy", but they will need to be electric strings on the acoustic since you will need to put the exact same set on the electric, so bronze (which is non-magnetic) is out of the question and pure nickel wound is ideal. You will not have the super-complex harmonics of fresh bronze strings, but that only lasts during the initial period of tuning instability anyway. The nickel's own brightness will outlast bronze in the long run. Almost always it's going to be a wound G on the acoustic so it'll be the same on the electric even if it's difficult to find in stock.
That's the only way your hands will be doing the exact same thing on either guitar.
Taken to the extreme, all practice and even rehearsal can be accomplished on the acoustic, and the electric only used for special occasions, performance or recording. You spend most of the time getting the most out of your hands and your super-familiar setup, extracting the tone from the acoustic rather than the electronics. You're going to need to play hard if you're going to have a decent volume on the acoustic like anybody else, but when you do break out the electric nothing changes for your hands. All you have is much more power than usual, don't let it make you hold back on the hard playing at all, just wail, and for that reason alone the electric always puts a smile on your face like it never did every time before.
Hard working musicians do take it seriously and probably do not smile as much as they should, but when you do see them smiling knowingly at each other it can often be because the groove or the tone are just better than usual right in the moment.
The hands can almost always use more improvement than the gear.