Which mortise lock/brand I should get to replace this one?
The one on the right (the old one) is an old Russwin Emhart mortise lock. You can still purchase ones like it from Corbin Russwin but they are quite pricey. If you want to replace the Emhart with the Marks Metro, a few shims and a new strike plate as well as some alterations to the door/door jamb should do the trick.