Your pc is pretty new and should support any new GPU, but, your built-in power supply is not going to run a GTX770 nor even a GTX760.
getting a new psu for a pre-built pc case might sometimes be hard because they might use a different size than what pc builders use as standard, but no matter that you will need a new psu to run the GTX770.
Also the space for the GPU, make sure that you have two slots in the back at the PCI-E connector so you can mount the GPU, also the GPU's physical size might interfere with something, you should measure out the width and lenght of the card, inside your case to check (ASUS should be the smallest of the two and faster out of the box by a little margin, though the MSI is probably quieter, since they actually used their new cooler for this card, not the old one, compared to ASUS's old cooler on theirs (it's a good cooler, but the task it's been given is the hardest it ever has been given).
So
1: check slots, size compability for the gpu
2: check PSU size and look for atleast 500w with a 80+ Bronze or higher rating (the XFX Proseries XXX Edition 550w is very good and very cheap!)
3: choose between ASUS quality which will last and very slight speed bonus or MSI with their new quiet cooler, which would be more silent in games.