Since the end of the James era at Washington here are the cold hard numbers:
WSU: 93-84 UW: 95-86-1
WSU 3-2 UW: 2-6
Rose Bowl appearances
WSU: 2 UW: 1
You would be hard-pressed to argue either is the "superior" program. Its been very even over the last 16 years. This idea that UW people have that UW is innately better is based on one great coach.
In fact, let's look at the two programs' total records since 1925, omitting the James era of 1975-1992 for both schools.
A whopping 31 victories more. Other than a great era led by a great coach, the series has been slightly edged by the huskies. They are not in the likeness of truly great football programs, no matter what they say on KJR. (AHH, Done.. this took about 2 hours to do....)