Ken's got it right. NCT on the west side of the river is dry, markedly less traveled and hilly. I think about 13 miles if memory serves. No views, a forest walk and more solitude. You'll be on a hard dirt trail with occassional sandy spots and occasional 2-track crossings.
The MRT on the east side of the river has very scenic overlooks of the river and is very popular. Weekends and color-tour time are pretty busy. It's shorter than the NCT by 2-3 miles. Relatively flat, walking the bluffs. Hard dirt path, some swail.
I've had good luck parking at the Red Bridge (name?) and walking north up one side, south down the other. There is a hand pump for water at the bridge camp site. A nice two-day one night trip.