If you take SQ you can neither use the First Terminal nor the First Lounges at FRA unless you depart on a LH First flight afterwards!!! So, that will be the Senator Lounge for you in that case. If your connection time is short that doesn't really matter because Senator Lounges are okay with showers, ... .
But if you tend to stay longer at FRA you might like to take a bath and eat and drink "in style" in the First Terminal / Lounges. ^ It's up to you!