I level all my DoH and DoL together (as can be apparent from my Lodestone profile) and it's really convenient. In addition to sharing gear, you'll find that your Leve destinations are all the same because the classes are all in the same range, and you almost always are able to make everything you need all by yourself. (There are one or two exceptions but that's all.)

But if you're open to the idea of buying materials, there's nothing wrong with leveling one to 50 then the next. Just understand that most of the times the gil reward from Leves will not cover all of your materials costs if you're buying all the raw materials and intermediate items.