The problem is that you're trying to do things that are hardware intensive without spending money on hardware. Will either of those systems work for your purposes? In the most technical sense, yes. But you'll be fighting with them pretty much the whole way.
AMD CPUs are going to be woefully inadequate for video editing, the 5400rpm hard drives are going to be a huge bottleneck, and laptop screens are just plain bad for getting an accurate image.
Ideally what you're going to want is an Intel processor (preferably a dual core), at least a 7200rpm hard drive and possibly a second drive (you can at least connect it through USB 3.0) so that you're not rendering to and from the same drive, and honestly, an NVIDIA GPU is ideal for at least Adobe Premiere. AVCHD is absolutely punishing even on modern hardware without some kind of hardware acceleration, and being able to use the Mercury Playback Engine is the difference between editing in realtime and not editing in realtime.
And what about this laptop - ASUS N53SM - Intel® Core™ i7-2670QM Processor (6M Cache, 2.20 GHz), 4GB DDR3 1333 MHz RAM, 500GB HDD, nVIDIA® GeForce® GT 630M 2GB ?