Can these PSU's handle an HD 6770?

Either one should have the power needed, Raidmax and even Cooler masters lower end are not always recommend, but as long as they deliver the labeled current, i see no reason for the system to not have enough power(your system should not max out either unit).

I do not like that Raidmax does not show a combined power for its 12 volt rails, but it may be the design is actually a big 12 volt rail with both rails being able to hit max, but without an actual number, its a bit harder. The lack of auto select for 120-240 volt AC is another not so good sign

The cooler master lists a better efficiency and should run cooler and draw less power from the wall.

A 6770 is not a power hungry card by any means, neither is your cpu(its not super low powered, but its not a power hog either).

I would estimate your system would not draw over 250 watts on the 12 volt rails at a very high load. I am NOT saying to get a 250 watt power supply.

If you do not plan many upgrades or massive overclocking, you should be fine, but if you plan some upgrades, look at some of the more expensive units from Antec/Corsair/Seasonic ect. They cost more now, but can be used for your next system.