I need to move my home networking equipment. (If you are married, you'll understand)

There are 2 locations to choose from. One location requires me to run longer CAT6 cables. 7 of them. The other location requires me to run a longer RG6 cable. (the CAT6 runs would then be about the shortest they could get)

So, I guess I need to know which can handle running parallel with power cables better, 25feet of RG6 or CAT6?

The parallel with power cable is only for about 6-8 feet, but that's already more than it should be for CAT6. It's an old house and I don't feel comfortable drilling more holes in structural beams than I need to.

How much longer is the RG6 too the modem going to be?
If it's too long it could cause modem problems.
I have had few issues with cat5/6 next too power wires unless these wires are feeding the newer style florescent lights. The ballasts seem to make an incredible amount of noise and it travels back along the wires.
If you go with cat6 cables get shielded cable!

Running one cable is always easier than running seven. Also RG6 has a metal braided shield built in.

-Otanx

The RG6 would probably be extended 20-30 feet and be running parallel to power most of the way.

20 too 30 feet is not too bad. I'd try it. Would be cheaper.