Can locals still hunt brown or grizzly bear themselves?
Or is it mostly guided like African hunting?

Karl.

In Alaska residents may hunt anything without a guide. I was stationed in Anchorage with the USAF and the rules allowed me to hunt like a resident after I was there for a year.

As stated above, residents can hunt brown/grizzly bears without a guide. In some places, where there is a lot of demand, like Kodiak Island, everyone has to draw a permit to hunt those big bears, including residents. In much of the state, there is a one-bear-every-four-years rule. If you shoot a brown bear in one of these hunting units you have to wait four years before you can shoot another bear in one of these areas. But, there are plenty of places in Alaska where you are allowed to shoot one brown/grizzly bear every year. So, if you are really wanting to shoot or at least hunt grizzly bears, there is always a places to go...