I haven't had any problems running both.  I have a few that do, because I'm finding the new designer to be better for public facing forms, but so many of my internal forms need the flexibility of complex Javascript, so I have several that submit as a new designer form, and then assign tasks to staff as classic designer forms.  The only thing that I've found frustrating with this is not being able to copy a form from the new designer and switch it to classic, so if I need a similar form, I have to rebuilt it from the beginning (copy in all the fields from the variable picker).