The LH First Class Terminal is really a unique travel experience. The extremely easy and personalized passport-processing attention, the FCT limo ride to the plane (which I assume but am not certain you'd get on an intra-Germany flight), the nice meal selection, the choice of fine Scotches and other liquors at the bar (if you care about that) and other nice touches arguably make this the premier travel lounges in the world (though I haven't experienced Thai's new F lounge in Bangkok). If your FRA layover gives you at least three hours to enjoy it, it's an experience to relish.

BUT if such perks don't mean much to you, I'd say go with UA and the single connection. The double LH connection is a bit of a hassle and a slight extra risk that things can go wrong on your itinerary. And even though I heartily agree that LH F service and food are better, personally I greatly prefer the UA suites to the side-by-side LH seats in F.

As already indicated by most other replies to your post, however, YMMV.

Happy trails, whatever route you go!