I've done both directions to JNB a few times from Denver. The layover in FRA is huge, you arrive early in the morning and depart at 10:30pm. Although the former Astron Hotel (I believe now the NH hotel) is just 10 minutes from the airport and I got a nice day room for around 50 euros in January.

Personally, I prefer east because I arrive faster, only one change of aircraft and no leap-frogging across the pacific (although SQ0019 has leveled the playing field a bit). You can also use your SWU to upgrade on LH, something you cannot do on SIN.

You might consider RTW tickets too, you are just about halfway around the world now, they are much cheaper (ordinarily) than round-trips and you could try BOTH routes (oneway).