Does it take more air or lung capacity to play the trumpet or sax?

The trumpet and sax use their air differently. Any musician needs to use as much lung capacity as they can. If the trumpet takes more air to create a note, the sax player should be able to play longer phrases. However, I use just as much air to play a sax as I do the trumpet... I just use my air differently. All musicians use all the air they can. As I said earlier, the oboe is the one exception, where there is so much pressure in the instrument that players blow out their air before they play.
If you want to play a wind instrument you're going to have to use a lot of air... the plus side is you'll improve the entire portion of your body dealing with breathing... including your heart. Remember wind instruments help kids with Asthma!

For the Trumpet-- Yes.

Sax--Not neccessarily... though it is important to have air circulation through your lungs. You don't have to blow that hard if you bring your instrument up instead of looking down at your music. I was always taught that and it works. Also, blow faster air for high notes...high notes on the trumpet need lots of fast, flowing air, so BLAST it out.

It may take some time to gain the lung capacity you need, but you'll get there.

Trumpet. As a long-time trumpet player, I can tell you that all BRASS instruments in general, take more air. (That does NOT mean they are harder or easier!)

any wind instrument takes a good lung cappacity, but when learning to play, and playing on a regular basis will improve your lung capacity.

I play the trumpet. It really depends on your mouth. But I'd say the trumpet probably does.