I guess there is a slight/subtle difference between the two, but also wondering what is the preferred/acceptable way to express this to someone who is a good friend (not just an acquaintance). Ideally it should show some concern but without being forceful or commanding.
The expression「無理しないで」is used in most situations for showing concern for someone who may expose herself/himself in doing an "impossible" activity that pushes them to their limits while a more refined 「ご無理なさいませんよう、ご自愛ください」could also be used. 「ご無理なさらずに」 which literally translates to "don't do the impossible" is adopting 「なさる」as an elegant way of saying「する」。
If the intention is to express concern for someone healing and recovering their health from sickness one could use 「お大事に」as a neutral and all-situation expression or a less formal 「早くよくなって下さいね」。