The AT3035 is flat up 15,000 Hz compared to 6,000 Hz for the C1. The C1 is hyped in the high end with a +5dB hump around 12,000 Hz. I would expect it to be the more sibilent of the two.
The AT puts out 25mV compared to 14mV for the C1. The AT signal to noise at 82 is much higher than 77 for the C1.
The bummer (for me) is the AT3033 is an electret, and the C1 is a true condensor design. This is a personal issue for me with electrets... YMMV.
From what I read here, the C1 is more hot in the in the highs, and this will limit its use, such as being a poor choice for cymbals and overheads.
In the end, auditioning them both is the only way to know for sure.