Here I will summarize some of my _current_ expectations on what really affects the electric guitar sound - this is what I currently think but always open to new discoveries. In no particular order, and assuming amph and strings etc. are the same.

Overall, if I consider the big picture including the player and the amp, it might look something like this for the percentages of what is important:



But the following disregards the player and the amp completely and just considers the actual guitar as an instrument:

Neck: – the biggest structural differences

- Neck build and material is the single biggest factor in setting the basic sound of the guitar (dark with rosewood/bright with just maple/spanky/middy etc.) and much of these also carry to the amplified sound
- Scale is also an important factor with a Fender scale giving a snappier basic quality, and e.g. a strat loses it's spankiness even when simply given a tilt-headstock. In other words, headstock string angle makes the guitar sound tighter with less 'jangliness á la strat', and a shorter scale also lessens the same. The main reason a Gibson-scale axe is hard to make sound like a Stratocaster is actually the scale & the headstock tilt and also neck material matters.
- A bad saddle is a bad saddle and kills the sound easily, but I think I prefer plastic or something over bone on electrics, bone can make the sound a bit too cold.
Overall the neck is what both vibrates and has the most contact with the strings, and for this reason is the most important guitar part by far, and the differences in the neck also carry through to the amplified sounds noticeably.

Body: – less important than is often thought

I have found that body materials and shapes have surprisingly little effect on the sound. As long as the material is consistent, it seems to sound good. The less consistent it is, the duller it becomes, but that too can sometimes be an OK effect. A plywood body can make a strat sound much more like a Les Paul for instance, dulling the effects of the strat-style neck. But, basically, most any material from plastic to aluminum to stone can work quite OK for body material, it really doesn't seem to be significant at all when amplified. If you change a strat body to a mahogany one, you'll notice a difference acoustically but most people if not all can't tell a difference amplified. Of body wood effects, it seems to me the structure is more important than the materials. For instance a maple cap to which the bridge is installed, does have a noticeable difference over all mahogany, but indeed I believe it is the change of materials under the vibration path rather than the actual materials itself that changes the sound. Hardwoods are the only thing that seems to really sound clearly different; an all-maple neck- thru for instance is indeed very tight sounding; but again that is more structure than material.

Furthermore, tremolos and fixed bridges, when well done, can change the sound quite little too in the equation. The bigger the mass and sturdier the pivot point to the body, the better the strings are held in position which means they can vibrate more strongly without being dulled, and the 'bigger' the guitar can sound; often also acoustically it will sound louder. But amplified, the differences can be small, basically only noticeable by usually getting a bit better sustain from a fixed vs. a floating bridge. Swapping trem blocks around seems to be mostly about that mass - the more mass you have, the better vibration/sustain, but it seems to not affect the basic sound really. A bad, soft-metal Floyd will make a guitar sound much weaker and thinner, but when it’s properly done, a Floyd-equipped axe can indeed rival hardtail sustain and sound at least when amplified.

EDIT: I have very little experience about semi-hollows etc. but overall, my understanding is that in cases of neck-thrus with PU's on the actual slab, the empty 'wings' affect the amplified sound very little, and I would venture the main reason for any changes is the lack of mass, resulting in a more 'airy' sound which can have lots of bass though because the neck slab allows for good vibration throughout. If pickups are mounted on thinner 'cap' the results are much more pronounce with a tendency to feed back quite easily and the sound produced can be quite microphonic and acoustic as well, depending on pickup type and coil looseness.

EDIT: the mass idea is further reinforced by a simple test - strum the guitar and press the body end against most anything with a larger mass, and the sound is immediately amplified and much deeper, regardless of the mass material. Press against a leather sofa - works well. A sturdy wooden cupboard - works the same. More mass equals more power to the sound; however some woods like mahogany have a structure that rather dampens vibrations than reinforces them - it may be that mahogany bodies may be more lively and acoustical the lighter they are for that reason. Mahogany was originally used to fight feedback and remove unwanted vibrations in guitar bodies, after all, so it can work to dullen the sound.

Electronics: – this is far more important than any wood etc. issues

These are easily the most important factor in the sound, quite naturally. Assuming there is nothing fundamentally wrong about the guitar, the electronics (pickups) govern the guitar sound by a whopping percentage. If the neck is like 70% of the acoustic sonic basics, the neck and body and all structures in total are only something like again 20% of the finished sound, if that. Pickups are like 70% of the entire sound all alone.

There are many basic pickup types that sound very different, and these + the actual output of the guitar are the most important factors. If you A/B pickups with very similar structures and outputs, there is VERY little difference between most any manufacturer etc. as long as we're talking generally well made stuff. Some cheap ones with dubious metals etc. can sound totally off the expectations, usually way dark. The bottom line is, if the pickup is fine and OK made, it makes no sense to change it to something just similar more expensive - only when you want a clear correction in its properties and/or a tonality change it makes sense. Even then in many a case you will achieve a bigger change in sound simply by adjusting the pickup distance to strings or even the individual polepiece heights, which can affect the overall harmonic balance quite a lot.

Shortlist for electrics part:

The pickup type is the most important (bucker/single/p90)
The next big change is operation (active/passive)
Output level is a huge factor
Pickup height(polepiece heights) are also absolutely pivotal to the sound produced, affecting also output.
Covers change the sound noticeably
Magnet style is also noticeable (alnico etc.)

Of other guitar electronics, it seems that tone circuits do change the sound some; omitting everything does make the sound a bit more attacking and screaming. It's a sutble difference but I'd venture it's bigger than changing body woods. Of course, not everybody wants the sharpest possible attack etc.

But all in all, electronics can also change the sound drastically with boosters, EQ's active or passive etc. I also know some people who have rigged their guitars to work in balanced mode using XLR cables and swear by it.

Please feel free to comment and/or make suggestions or proof to reinforce the ideas presented, or to the contrary, or on what I have omitted.