I would say taking everything into account you'll be better off stciking with the 350.
Firstly while as a general rule big pixels = less noise, you also have to factor in the fact that
1 - the 1D uses a Panasonic CCD sensor not a CMOS - in Canon's hands at least, CMOS has proven to be inherently cleaner.
2 - the 1D sensor is only 4mp. If you were to reduce your images from the 350 to 4mp, you'll find that these will look sharper and cleaner anyway
And of course there's the fact that the 1D dates from 2001 - Canon has done a lot to improve image quality across the board since then. Color and dynamic range will are probably better in your 350.
A camera dating from 2001 could have quite a history - you may want to consider the cost of a shutter replacement if this camera has been used even moderately (10k shots per year and it will have exceeded expected shutter life).
Finally, I'm not sure this camera will work with modern CF cards - it uses type I or II
- with a maximum size of 2gb. I suspect it won't recognise any cards currently on sale.
Colin K. Work, Pixstel