Two different types of mic, NT3 small diaphragm, NT1, large. Usually used in a different application. One or the other may sound better for you, as a vocal mic. I've liked some of the results using a C1000 (another small diaphragm, don't own a NT3) on vocals, and I also like the NT1 on vocals, but it all depends on the song and the sound your after. Ideally, try both of them out and then decide.
Generally speaking, proffessional studios tend to use large diaphram condensers for vocal applications. The NT1 would probably be a better mic for your purpose.
Of course, I have to reccommend the Audio Technica 4033a.. it's a big favorite around here, and it really is an amazing large diaphram condenser for the price.