AFAIK, homeless problem scales with population size. So if you divide by population size (which those values do), the value should stay roughly the same.
What are the factors that make this untrue?
Cost of housing is a big one. Low housing costs and plenty of space available make the homeless problem both less likely and easier to deal with.
Yep, there are plenty of outlying areas in LA that are still not expensive in the same way SF is - LA is just much, much bigger. So you can hang on with significantly less money. Still, it's an interesting question.
So really, a more meaningful comparison (if one is resigned to handwaving about tax bases, without delving into details of city finances) for SF would be Boston, with 865,000 people out of 8.2 million for its CSA.