Which is better for recording vocals?

Both work. The WA-47F adds color that suits loud, dynamic singers. The AT4050 is more neutral and lets you pick omni or figure-8 for a roomier sound.

Which handles loud sources like kick drum better?

The AT4050 has the higher max SPL at 149 dB, so it takes extreme levels with more headroom. The WA-47F is still built for kick drum and handles it well at 137 dB.

The AT4050 has a longer record of daily studio use, including reported drops, and more owner ratings behind it. The WA-47F is solidly built but has a smaller track record.

Is the WA-47F worth stepping up to from the AT4050?

Only if you want its specific FET character on vocals and drums. The AT4050 is more flexible with three patterns and a wider frequency range.

Do both need phantom power?

Yes. Both are condenser mics that run on 48 V phantom power over XLR.

Can I use either for instruments other than voice?

Yes. The AT4050's patterns suit acoustic guitar, piano and room miking. The WA-47F works well on guitar cabs and drums.

Audio-Technica AT4050 vs Warm Audio WA-47F

The AT4050 is the safer all-round studio condenser: three polar patterns, a shock mount in the box, and a long track record of surviving daily use. The WA-47F is a single-pattern FET mic built to flatter loud voices and kick drums, with a fixed cardioid capsule and a heavier body. Buy the AT4050 if you need one mic for many sources; buy the WA-47F if you want that 47 FET character on vocals and drums.

Choose the AT4050 if you record several sources with one mic and want switchable patterns plus a shock mount included.
Choose the WA-47F if you mainly track loud vocals or kick drum and want a fixed-cardioid FET mic with that classic tone.

Prices

Audio-Technica AT4050: $576.75 at Guitar Center (last seen Nov 9)
Warm Audio WA-47F: $599.00 at Front End Audio (checked today)
Difference: the Audio-Technica AT4050 is $22.25 cheaper than the Warm Audio WA-47F at the latest prices (Nov 9 and Nov 10)