Both books have the same target group, and the scope is similar (classical logic, modal logics, conditional logics, and a bit of set-theory). However, there are some interesting differences: Sider's book includes several quantified logics, while Priest's book is propositional logics only. Interestingly, Sider's book also drops out relevant logics altogether. I suspect that these aren't important for the kind of philosophy Sider has in mind. To compensate, however, Sider has included interesting chapters on two-dimensional modal logic, and he also provides the reader with a bit of natural deduction (although not for any interesting systems).
Of course, this comparison is just by glancing over the material in the new book. Hopefully, I'll have a closer look in the near future. Meanwhile, find out for yourself.