Tasha's and Xanathar's subclasses in 5.5e

I've been searching and can't get a straight answer. Do the subclasses from both books hold up to 5.5e subclasses, and do any not function at all anymore? If they are underpowered, are there any easy asjuatments that can be made to make them more in line? Are they worth getting or should I wait and see if they revise them?

1) “Do the subclasses from both books hold up to 5.5e subclasses”- Not sure what you mean by “hold up”, please elaborate.

2) “do any not function at all anymore”- Nothing about the core class changes in 5.5 keeps a 5.0 subclass from functioning. There’s some 5.5 subclasses that won’t work perfectly on a 5.0 class chassis, such as Rogue ones that add to the Cunning Strikes feature introduced in the 5.5 version of the class, but that’s it.

3) “If they are underpowered, are there any easy asjuatments that can be made to make them more in line?”- In general I’d say there’s no significant power disparity, and there’s no simple and broad way to attempt to tune up subclasses in any case.

4) “Are they worth getting or should I wait and see if they revise them?”- If you mean the ones in XGtE and TCoE, I’d say get them now if you’d like. There’s a lot that haven’t been updated yet, and current releases seem to be aimed more at creating new subclasses than updating existing ones, so you could be in for a long wait.

Hold up I specifically meant power-wise, not that I'm intending to min-max, but I don't want to stumble into an underpowered build. And I'd heard about circle of Shepherd Druid being a little borked due to conjuration. I just mostly wanna know if they'd still be satisfying to play imposed into the 2024 rules.

The only 5e subclass that I'd say doesn't work super well in 5.5e is the Circle of the Shepherd Druid from Xanathar's Guide to Everything. This isn't due to anything in particular about the new Druid class; it's just that it depends very heavily on the use of spells that summon creatures, and its features work best on spells that summon multiple creatures. While there are still summoning spells in 5.5e, many of the spells the Shepherd Druid relied on have been changed in 5.5e so that they create area effects rather than summon creatures, including one specific one that's referenced by name in the highest level feature of the subclass. This is not to say you can't play a Shepherd Druid in 5.5e, but you'd have a lot fewer options for summoning spells, your features that improve them would have less impact, and your level 14 feature wouldn't work at all as written.

That's an outlier, though; in general, the 5e subclasses that haven't been updated will work just fine in 5.5e.

Power-wise, it really depends on the subclass. Some pre-2024 ones are still fine, while others are weaker than newer ones.

It heavily depends on the class.   Ranger is a mixed bag, being functionally better in some respects and objectively worse in others. Yet the tashas ranger is marginally better because of how resources are used.

Spell casters in 5.5 have fixed number of prepared spells, but 5e and tashas scales off of main stat for spell casting, and has less regulated subclasses  

You’ll find endless edge case comparisons like this all over, since 5.5 shifted most of the power out of classes and moved them to spells and spell access. So there is no solid answer, since the question of “underpowered” is a build specific question requiring looking at 2 variations of  a build and comparing it to other classes or party members. 

But as a rule of thumb for 5e, access to spells trumps all first party subclass features, with only a few notable exceptions. And in 5.5e access to spell lists is better than spells that replaced class and subclass abilities.