: Does the 7th major scale note resolve more strongly to the lower tonic (note 1) than the higher tonic (note 8)? Does the 7 resolve more strongly to the 'lower' tonic (1) than the 'higher' tonic? I used the word resolve as

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It's kind of analogous to ionic bonding in chemistry. Take Sodium (Na) and Chlorine (Cl), for example.

Generally, students acquire the misconception that when Na and Cl react to form NaCl (commmon table salt), Cl simply removes an electron from Na, forming Na+ and Cl-.

But that's not strictly true.

Electrons actually exist in probabilistic regions, meaning there's a certain chance that an electron is in any position, rather than a defined, singular location. Because of the Octet rule (and/or other reasons), the chlorine atom - having 7 valence electrons - much more often takes on an 8th electron rather than losing all seven to go back to 0 valence electrons (which would then mean that it actually had 8 again, but you get the idea). Applying this to NaCl, the individual chlorine molecule attracts the electron so much more strongly than Na that the electron is extremely likely to be "part of" the chlorine atom at any moment. This inequality is so pronounced that we observe the Cl ion to have a negative charge. This post has some more in-depth information, as does the rest of its host question.

To bring this rant back to Music Theory, no, there are no hard-and-dry rules on how the 7th degree, or any scale degree, resolves. But we observe that nearly every time, the 7th scale degree resolves to the octave rather than all the way back down to the lower octave. A bunch of explanations exist for this, and as others have noted, smaller movements tend to be observed as "smoother" resolutions, but my point is that the 7th degree is commonly said to resolve up to the octave because that's how it happens nearly every time. If you feel it works better down to the octave, by all means give it a try, but recognise that you may be mistaking the resolution's effect with that of the effect of having the lower bass note, and that you may achieve effects that you did not intend or did not desire.

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The question is, does the 7 actually, technically, resolve more strongly to the 'lower' tonic (1) than the 'higher' tonic but compositionally it sounds better to resolve to the upper tonic?

I don't understand your distinction between what's "technically" right and what's "compositionally" right. In music, composition comes first, and theory is used to describe the composition.

So the reason we say that the 7th scale degree resolves up to the 1st is because that's how composers have traditionally resolved the 7th scale degree.

For example, ignoring the 7, if C4 (middle C) resolves more strongly to C4 than C5 then it would stand to reason that B actually resolves better to the lower tonic but it's always listed as going to the higher tonic because it's more compositionally useful.

This is not a good example because there is no tension between octaves. The concept of resolution in Western music theory is based on the idea of tension between the various notes. If you feel that C4 to C3 is stronger than C4 to C5, then you can certainly use that preference to influence your personal compositional style, but it is not something that has yet been incorporated into standard music theory.

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When talking about resolutions, most if not all times the smaller the distance is the better resolution. In this case hands down the leading tone wants to resolve step wise up, not down a major 7th. That resolution would be jarring to most.

To take a step back, there is no difference from a harmony perspective from any octave equivalence in terms of generic harmony so 1, 8, 15, ect are all treated as the root note your scale/key so the idea 8 would be weaker than 1 is not correct in general terms and in this case 7 will really want to go to 8.