That second laptop is better in every way. The better processor with an actual quad core will be particularly helpful for emulation, though I'm not sure it matters much for PS2. Getting an actual gtx card (though it is the lowest mobile tier) will make a solid difference from a non gtx (which aren't meant for gaming).
For comparison, my current craptop is a bit weaker than that MSI (i5 4210u, gt 840m), and I can play NBA 2k15 at 720p high settings. Surprisingly I was even able to run GTA V (very stable and smooth too), though at low-medium settings at 720p.
The 950m will be reasonable step up from that, though.
Here are some benchmarks from various games. Looks like you'll be able to max out Fifa 15.