Certainly there will be competition for both moisture & nutrients. I have a couple of grasses planted in a similar situation and they are not as vigorous as they might be.
You might just have to give them a little more TLC over the growing season or as you suggest, move them to a more ideal location.

And yes, I am growing both of these in my zone 5 garden. The Saccharum ravennae is the more tender of the two & I often loose sections of the clump AND it is very, very late to appear in the spring. You may be pushing it by planting that one this late in the year. A little mulch couldn't hurt.
A.