When having the choice to use a Hook or Advice to manipulate a certain package, what should you do?

Hooks are always better because they break less. If the author provided a hook, then the author expects user code to run. Advice, however, can have unexpected side effects. Advice should only be used when no hook is provided.

The problem is that advice subtly changes the semantics of the commands it advises, and this change is not visible in the code of those commands. So it works, but it’s better to fix those commands directly. That doesn’t mean `advice.el’ is evil, but that it should only be used when you cannot change the command; for example if you want your package to work with older releases.

Advised functions are difficult to use with the debugger.

Extra special care needs to be taken when advising Emacs Lisp primitives. The special case of advising primitives is further explained in the EmacsLispReference.

What other people have said

Here is StefanMonnier’s strong ‘advice’ advice from mailing list

`advice' is a sledghammer: it's the last resort before
modifying the source code.

Advising is a source of major headaches because of unexpected
interactions with other pieces of code...
Advice have to be written *extremely* carefully.
I.e. if you can do it without `advice', then don't use `advice'.

And this is what RichardStallman said 2005-03-03 about Emacs developers (not users) advising Emacs primitives:

Please do not think of making any part of Emacs advise primitives.
That technique should never be used, because it causes confusion.  All
code in Emacs that advises other parts of Emacs was installed without
my knowledge.  It is a bug that ought to be fixed.

And this is what RichardStallman said 2005-08-03:

No!  Emacs code should not use defadvice.

When you're trying to make improvements in Emacs or fix problems in
Emacs, please do NOT think of defadvice as the way to do it.

And this is from an exchange on, 2007-06-02, between KevinRodgers and EliZaretski:

Kevin> I think RMS' position is that defadvice should not be
Kevin> used within Emacs itself.  But the inclusion of defadvice.el
Kevin> in Emacs is tacit acknowledgement of its usefulness

Eli> You are right on both accounts.  And I see no contradiction
Eli> between those two, because RMS never said that defadvice is
Eli> not useful.  His position on not using it within Emacs itself
Eli> is because doing that obscures how things work, which is bad
Eli> from the maintainability point of view.  FWIW, I agree with that.

Enough said. 😊