What are the advantages of booking a Lufthansa flight on the UA web site as opposed to directly at LH.com?

I have been eyeing flying on the 747-400 for one last trip and I can apparently book a business class JFK-FRA vv one either airline's web sites.

I am planning on opening a MileagePlus account and I see how booking on the UA web site gives the flights more credit for PQPs/PQFs on MileagePlus. Apart from this, is there any other advantage?

I don't have any status on Star Alliance. I am a SkyMiles refugee. And over at DL, I usually have been booking KE flights on the DL web site because I get more baggage allowance and also am allowed more flexibility with rescheduling/ cancelation (DL vs KE policy).