It seems that Brown is pro-states rights. It also seems like she is, at least most of the time, a stict constructionist. And I think her judicial record may be significantly more diverse than Judge Souter's in NH. California, being the largest state, and one of the wackiest legislatures and many wacked out town councils, is going to give the state supreme court lots to rule on. In a way, it's almost better than a justice come from California than NH. In NH, people aren't as wacky, and they don't pass wacky laws, so you never really know if a justice is going to vote the right way. In California, the supreme court is going to have to rule on all kinds of things.
Her ruling on the assault weapons ban is a bit questionable, but we don't know all the issues involved. We don't know what the briefs argued, as I'm sure no one here has read them yet. In particular, we don't know if the briefs challenged the law on second amendment grounds, or on state constitutional grounds.
In any event, before she's nominated, I'm sure that there are volumes that Bush's staff would be able to read to get a clear idea of how she really thinks. Because someone's ideology can't hide in California the way it could in New Hampshire. There's way too many nuts passing laws in California.