Not a Huge difference from the 300C, I'd guess
Yes, as you move up the performance ladder, certain things get more expensive. However, I'd expect that the SRT-8's drivetrain will be pretty bulletproof and, as is the case with most modern cars, fairly low-maintenance.
Tire Rack lists Goodyear RS-A all-season tires in the 245/45/20 size for $178 (no listing currently for 255's), which is about the mid-range for high performance, low aspect ratio tires. I was actually surprised that the cost was this low. All-seasons will give you a longer tread life than summer tires, but you'll lose some warm weather, dry pavement adhesion.
As far as the brakes are concerned, I wouldn't expect that high-performance pads for the Brembos would be much more expensive than regular pads, and the cost of labor should be more or less identical. When you start getting into other brake components, you'll pay more.
A lot depends on how you drive the car, but I wouldn't expect that maintenance will be significantly more than a standard SRT-8, unless you drive aggressively most of the time. However, the SRT-8 will be more expensive in terms of the initial cost, insurance, and fuel. These factors will probably constitute a greater part of any overall difference in operating costs than will maintenance.
I'd also expect that an SRT-8 will depreciate less rapidly than a standard C if you treat it well. If I'm guessing right, this would, of course, offset some of the higher operating costs.