Actually I would fly JFK-FRA-SIN if I could only do one of the two. The VS lounge at JFK is excellent, whereas I find TPR too hot.

I believe arriving from the USA, that there is no transfer security requirement at FRA. Arriving from SIN at FRA, there is an escort to a private security lane with a single screener that can be extremely slow. Plus FRA's magnetometers are set to an overly sensitive level that often leads to a very intrusive pat-down.