Which laptop is best?

The Acer Aspire 5551 is the better choice. The processors have same clock speed, and both have same amount of RAM, same hard drive, BUT the Acer 5551 has better graphics card. Even if all you are doing is light gaming, you generally want to avoid integrated graphics. The 5742Z has integrated graphics while the 5551 has hybrid graphics. Incidentally, if you don't know about hybrid graphics, I'll explain. An integrated graphics card has no memory of its own and must share RAM memory with the CPU, a hybrid card contains some dedicated memory of its own(not shared with cpu) plus, some it also share with cpu. In the case of the 5551 above it has a Radeon 4250 in it which has 256 MB dedicated and then it also has another 1GB available that is shared. With hybrid graphics you can usually play most games to at least their mid level graphics settings while with integrated you can only play to low level if at all (depending on game).