You are right that
the AT4040 has a flatter response than the 4033, and IMO it is a little more versatile than the 4033. Both are great mics. For lead vocals, flatter is not necessarily better. I've done a lot of recording with most of the mics mentioned so here are my thoughts:
4040: Great mic to have around, you can throw it on a lot of stuff and it will be fine. Not my fist pick on most lead vocals but it will not suck.
SP C1: Oh the memories! Great little mic, but no U87. Has a ton of top end and is not very versatile...you won't be putting it on most instruments and get a very good sound (although it is great on the side of a snare). I had one rapper who loved it and sounded better on it than on any other mic. Most people sounded OK on it, unless they had a high nasaly voice.
Rode NTK: pretty sweet, but similar to the C1 in that it's not super versatile...but the sound quality is much better. Likewise, I had this one acoustic player/singer that sounded like a million bucks on it. It was average on everyone else.
Shure KSM27: similar to the 4040 in applications. Great mic for under $300 and sounds decent on a lot of sources, but not necessarily stellar
Shure Beta87 (a or c): awesome mics...doesn't look like your typical studio mic, but is a condenser, and does sound good. It's not real versatile but it usually sounds pretty good on vocals. It could do real well on rock vocals, and it could double as a live sound microphone. It's also more durable than most condenser microphones.
Also, check out the new Groove Tubes mics. They just released a new line at NAMM (it includes some of the old ones). In your price range you might want to check out the
GT50 and the
MD1b-FET. The GT50 is a little more open, with the MD1b having a darker, more vintage tone.