I've never considered Easy Bay because of its much higher crime rate. There is a reason it's cheaper. Maybe things are different now, but I wouldn't know, because I've never considered it.
SF may have crime but its nowhere near the danger level of oakland. IIRC, SF isnt even on the "top 100 most dangerous cities" list, but oakland usually is in the top 5.
So, yes- Big difference. 10x higher chance to get murdered in oakland than SF.
It's far wiser I think to use sites like http://www.trulia.com/real_estate/Oakland-California/crime/ to evaluate on a more granular level.
As you can see, there are areas of high crime density on both sides of the bay.
I guess my point is that a city having a high crime rate does not necessarily put it off limits; it may just mean that particular neighborhoods are off limits.
"PA is safe, just don't go to Philly", "Philly is safe, just don't go to North Philly", "North Philly is safe, just don't leave Temple's campus"... etc. It's all just a matter of scale. You could break it down by block if you wanted to.
Oakland is not the whole East Bay.
Oakland, Emeryville, Richmond, and San Pablo have high crime rates, sure.
The rest of the East Bay, not so much.
(And, of course, the East Bay isn't the only place one can commute into San Francisco from -- the Peninsula exists, too.)