You can do "see only current branch" with the little filter icon when you hover next to a branch. Although I do find myself getting lost amongst branches more easily compared to Sourcetree, I think there's some difference in how filters are combined that isn't ideal (but I can't remember specifics)
You can also go to View in the menu and click "Filter by active branch" (Ctrl+Shift+A).
Also if you, like me, wanted to blame or view history for specific files there does not seem to be a way by clicking in the GUI to achieve it. But by using Ctrl+P you get the command search and can search for "Blame" or "File history".
Another vote for Fork here. Used to use many different UI clients, including ST and Tower but left Tower for Fork. I still add P4 Merge as my external merge tool though. It seems to have the best algorithm and often solves conflicts automatically.