Depends on what your criteria for "best" is. What's important to you - screen size, outright performance, price/performance, camera quality, build quality, availability of accessories, long-term viability of supplier etc?
Personally I think the 'best' would be the S4 overall. The HTC One looks great but they've done an "Apple" and sealed the battery inside it. It's also very heavily customised so be sure you like the user interface before you buy one.
The S3 is still an ace phone and right now I think perfect price/performance. If I were on the market for a phone now the S3 is the one I'd buy.