I'm designing a phased array controller and as such includes a dozen splitters . The board dimensions are approximately around 10 - 11 cm and the RF traces are about 8-9 cm in length . Would differential pair routing offer significant improvement ? Would using a balun to convert the diff to single ended signal introduce any noise which defeats the purpose of using diff ended routing ? Operates in C band (4.8 - 5.4 Ghz)
So, in general: For RF signals, you'll have a properly matched transmission line, so that the only thing affected by the line length is the phase of the output signal relative to the input signal.
Since these lengths don't change during operation, you can calibrate that out once, and not care about it.
If your job, however, is to have a defined phase relationship between in- and outputs, you'd of course have to take care to properly choose and match lengths (but I guess you knew that).
Then, you forgot to mention the frequencies you're operating at. Of course, 9 cm means something different for the phase of a 10 GHz signal compared to a 100 MHz signal going through the same length.
Then: Your Balun question doesn't make much sense. You can have single-ended transmission lines on a PCB (typically, something like a single microstrip line, or a coplanar wave guide with ground forming the outer conductor), or balanced transmission lines, like a coupled coplanar line. You'd typically choose the transmission line type based on the thing you need to do, and the abilities of your production process and substrate material.
No, a balun will not change the performance you achieve with your circuit. The phase of each path will be static, plus or minus the impact of PCB manufacture tolerance, loading variation and component placement.
Using one single-ended transmission line or a balanced pair might result in some averaging of the errors, or might increase them - I expect the difference might be minimal unless you're cutting PBCs by hand...