General background.
The 360 can't be downgraded in dash via conventional means -- it has fuses inside the CPU that get burned when it upgrades (see efuses) so older stuff won't boot.
Naturally as time went on MS blocked various exploits. There are possibly 4 things considered in this
1) King Kong. The original homebrew exploit.
2) JTAG. The first homebrew exploit most met. Dashboard version 7371 and below will 99% of the time be what you want (technically it was not the dash but an update that came with it to another component, there are a few that might have been made already fixed but on a lower dash or had some weird means of updating that before the dash was). Blocked mostly before its main release but still had quite a few out there as there were enough offline/sitting in a cupboard/previously banned ones. Can be done with basic components.
3) RGH. The main current one, works differently on different boards. Needs a specialist chip.
4) The XGD3 DVD drive firmware update. Certain DVD drive models needed an update to their internal firmware to run the more modern game discs (MS tweaked the format to gain that little bit more storage). This can make aspects of key retrieval harder, and at the time then anybody with a drive flashed would have to pull it apart to update it themselves again afterwards which might have been annoying if it was not them that did it.
Any additional stuff is a historical quirk (for a hot moment there was a beta that did something later stuff did not whilst allowing certain games to boot on DVD modded stuff, and some stuff for DVD/video playback), though maybe you could run a demo of a blacklisted XBLA game that bypasses the demo wall. Nobody is really going to pay up for anything there.
Additionally some do like the older "blades" dashboard that looks somewhat different to the later versions (of which there are a few more) but it is not really a thing that commands a great premium, might get someone wanting it for a display piece though.
Naturally this is all tempered by the older models being generally noted as being loud as a plane and also prone to red ring of death/rrod. At this point for the original style of xbox 360 then I am not buying anything that is older than a Jasper (the last released model) and generally encourage others in that unless it is truly rock bottom price. Jaspers will also come with liteon DVD drives but eh, older models come with other things.
https://gbatemp.net/threads/guide-how-to-hack-your-360.334203/ has an older image but as this discussion does not care about the slim and lite (which has a circular power jack) then it is suitable for these purposes.
A Jasper that could have been JTAG hacked would mean you have lost a bit as someone would have probably paid extra for that, might have got if not more than a faster sale if it was a Falcon or Zephyr that could have been JTAG hacked. Though as noted above then it is not really going to be a massive premium compared to some hacked/hackable versions of devices as the RGH mod works reasonably well, is not that expensive and doable enough for most models of 360 out there today, technically comes with some perks JTAG does not in some cases (see dual nand such that you can dual boot to get online on an unhacked version) but nothing 99% of people will care about -- JTAG still does all the region free, homebrew, hacked games, any size hard drive, USB loading, XBLA, DLC,
cheats and such, even if it costs online. If for some reason you value online most will tell you just get a second 360 as stock ones of those go for not a lot really, DVD hack it if you are really bored.