The specs you are showing are almost the same. Unless there is something drastically different in the bus speeds they should run about the same.
The first one has a 9cell battery that will likely last longer than the 6cell but you can probably upgrade to a better battery in the second unit.
There is no DVD burner listed in option #1 - I would definitely want one.
I had an issue with a Hitachi HD with sound & heat (though it wasn't a laptop HD and I would be surprised if they would allow too much heat in a laptop), so I personally would prefer the Seagate in Option #2
Option 2 weighs an extra pound and a half and is wider and thinker which to me is worth it for ...
the biggest difference: extra 2" of display so I would go with option #2.
(Well the biggest difference might be price but I can't see that in photo #2

)
I also see no mention of how many USB2.0 ports are available - my nephews has 2 and I wish it had 3 or 4 so it may be important information depending if you add a usb keyboard, usb mouse, flash drive(s), laptop fan. Of course you can plug in a 4-port usb extender.
And ethernet connection (or even phone jack, though dial-up is almost dead) are not mentioned - you may want an ethernet connection if you ever want wired instead of wireless.
To be honest, since it has bluetooth I would recommend a bluetooth keyboard and mouse for wherever you are using it most. I had to use one of my nephews usb slot to add bluetooth for his keyboard and mouse but both of these have it built-in.