The other says that I will not be
able to notice an untucked carpet at all looks-wise, and the only
possible difference would be in 5 or so years its possible that the
carpet may need to be retacked if it starts to pull up.

Can anyone chime in with their opinion as to which is best. I'd
rather not spend the money to re-do the baseboard if I'm not going to
be able to see a difference.

I'd not remove the baseboard. Most that I've ever seen have not been.