I am personally a Corsair fan myself and I don't know too much about Mushkin.
Should I wait for the Corsair kit and possibly risk being late for xmas, or should I just take the Mushkin kit and finish the rig?
FYI The Ram will be installed on an ASUS P8H61-M LE Mobo along with an i3 3220 3.30GHz CPU (thats the best I could do on the budget I have for the build )
There is a good chance they both use the same module under the heat sink. Neither company is a manufacturer and both buy from the same OEMs like Micron, Elpida, Powerchip, Hynix ect. Both kits are rated the same 1.5v DDR3 1600 cas 9 and both have lifetime warranties. I would say you are good with either kit.