I was wondering whether there is a tonal difference between the type of dropping string resistor you use.
I can't say I've ever heard a tonal difference due to dropping resistor type. The "best type" is the one that yields the supply voltage you need and delivers sufficient filtering/isolation (meaning, the one that's the proper resistance).
It is my opinion after a long while messing with this stuff that tonal change/improvement is found by changing a circuit type or parts values; the intense focus on a type of part appears to come from those who don't know much about how the circuit work (i.e., the ones who want to "mod an amp" but don't know enough about the amps to make a real circuit change) or from those who are marketing to the first group.
To be fair, there are differences in the characteristics of various parts, and some can have a tonal impact. I'm simply saying my opinion is that the tonal change due to a part-type change is maybe a couple-percent, compared to a tonal change from a circuit change giving a 20-100% difference.
Example:
In a recent build, I used metal film resistors almost exclusively. It wasn't a "Tone!" choice, but because metal film has the lowest self-noise of all types except wirewound (but you can't readily get those above a certain resistance).
I used Solen polypropylene filter caps; some say they have a "sound" but I chose to use them where I could because they will never wear out and need replacement like an electrolytic cap. In one part of the amp I used a multi-section can cap because it didn't have the space to fit the very-large Solen caps.
For power supply dropping resistors, I used wirewound (for the low-noise reason). I didn't used the white cement-block types, and chose some black Dale wirewounds instead. Why? Mostly because they look prettier (at least I'm honest about the reason!).
I used some no-name coupling caps because they were cheap and had a polyester dielectric, which I thought would mimic 50's-60's coupling caps close-enough.
I used some expensive pots; in most locations their only benefit was that they're completely sealed and they feel nicer when turning knobs, but in a couple locations (bias adjustment and balance) the expensive type was the best part because they were screwdriver-adjustable and include a lock to prevent accidental changes.
Throughout I used some strips I made which were a single-row of turrets. I could have used terminal strips (would've been cheaper & faster), but I don't like the look of terminal strips as much (another cosmetic choice), and because a part change/repair is a little messier with terminal strips because of how the lead is wrapped instead of sitting in a hole.
I used Teflon-insulated wire in the amp, but the main reason was that the plastic insulation won't melt when you solder (plus I got it cheap, and in an array of colors for color-coding during wiring).
I was advised to use particular transformers and speaker for the amp, which turned out to be critical (in my opinion). For the output transformer I used a type which is "too good" for a guitar amp (rated for full power 30Hz-30kHz & bigger than the average 100w guitar amp OT for a 25w amp) but the choice likely contributed to the quality of the extreme-clean the amp gets. The speaker was also a full-range hi-fi type with high sensitivity which translated the amp's relatively low power into a lot of volume in the room.
I think you'll see a few things were chosen for a tonal contribution, but most parts were chosen for other characteristics (even if that was just "I like the way it looks"). I've arrived at my attitude towards parts types because I'd gone the route of using expensive tweak-parts (once including coupling caps costing me $20-30 each and resistors at $1-2 each) and found the resulting amps didn't sound materially better than if I'd used much cheaper parts.
But that's just my opinion.