It varies from shop to shop and depends on each other skill and experience. In some shops DBAs do not get any priviledged access on the machine, while others backup the sys admin and vice versa. This also depends greatly on your skills, experience and desire. Do you have the skills needed to backup a sys admin? If so, you will mostly likely overlap in many areas.

Where I work we have two types of sys admins. One manages the whole machine and another manages just the domain(A Sun Microsystem thing). I gather statistics on CPU, memory and I/O and how it relates to Oracle, while they focus on other aspects. I tell them how I want the I/O layed out and they implement.

Watch out there are many sys admins that think a database and a file server are the same and they are not. I have seen a DB machine set up like a file server and it was horrible. The way the sys admin came up with his stats was to move large files around and measure I/O. This is great for a file server, but horrible for a OLTP DB. So keep a watchful eye out for what your sys admins do, becuase it can come back to haunt you.