Over 95 percent of our web site traffic somes from Google search referrals, and less than 1 percent from Yahoo search referrals.
We submit site maps daily to both Yahoo and Google.
Any idea why Google is so strong and Yahoo is so weak?
I found it weird too. Actually I have similar statistics as you do.
To test, I just tried searching by Yahoo! a few really old threads (but very specific in topic) I posted a few years ago, by using a few very specific keywords. Both Yahoo! and Google got the threads. So it seems like the threads have actually been crawled. They just do not turn up early in the search results unless I am using very specific keywords. This seems to especially the case if I use Yahoo!.
For my personal site, awstats reported 1294 referrals from Google and 68 from Yahoo! for the month of June. For the keyphrase "perl tutorial" that gets the most referrals for me, Yahoo! turned up my site on the 6th page while 2nd page for Google. I did not perform any SEO intentionally.
Well, of course, if a search result appears on page 5 or later then we can safely assume nobody is going to see it ...
Why is that? Do some sites optimize better for Yahoo and others for Google? And, if you are optimal (by design or accident) for one search engine, you are suboptimal for another?
I think they use different algorithms for prioritization that gives rise to the difference. However, the exact mechanics are beyond me. But I'm still inclined to think that Yahoo! seems to bias keywords.
For long time in the past, I got more hits from Yahoo! compared with Google. I think the reason was that many URLs of my site bear ".pl" that drove Google away, but apparently Google changed something from last year onwards that I got more and more hits from Google and dynamically generated pages and URL seems to be no longer an issue. At least for me.
Maybe if a site runs Google Adsense, Google places them higher in the rankings and ditto for Yahoo, publishing Yahoo ads?
I run neither ad service and still that does not explain the difference ....
How about because nobody actually uses anything but Google any more.
+1 for reason 
But I think that SearchMonkey will be BIG step forward.