Hi Valo,
I think the best way to compare the two will be via Pros and Cons, based on the info you've given for your parents' usage I think Even the lowest spec 13z will suit them nicely. It would also improve battery life a bit more due to the lower power from the CPU compared to the one I have but still be beefier than an Atom.
HP 311c:
+ More portable by about an inch (W/L).
- Thicker at the back.
+ Longer battery life due to using a 6cell as standard, probably 6hrs vs 4hrs.
+/- Keyboard keys are large but quite close together, this may or may not be an issue, preference I guess.
- Atom CPU is quite sluggish, I see this even more now since getting the 13z and seeing how fast that is in comparison.
- 3GB ram max supported as only 32bit OSes are supported by Atom.
- Some driver bugs with nVidia's drivers causing slowdowns for people if some chipset drivers are installed, best to leave Windows 7 drivers installed if installing Win7
- No DVDRW drive
+ The speakers on the 311c were very impressive as was the headphones out, I prefer the sound on the 311c than on the 13z but I can live with this.
- Laggy trackpad
Dell 13z:
+ More professional and sleek looking.
+ Express charger feature where 80% battery can be had within 60mins of charging.
+ DVDRW drive included.
+ Intel ULV CPU is much nicer experience over the Atom, Win7 loads super fast and runs super smooth.
- Viewing angles are slightly worse than the HP 311c screen, both are LED backlit though and both have very nice colours
- The 4cell battery is what you get as standard, they also have an 8cell battery at extra cost and that sticks out an extra inch at the back. Worth keeping an eye out for 3rd party batteries maybe a 6cell down the line.
+ The keyboard is much more spacious and natural than the 311c, easier to type.
+ The trackpad is excellent, no lag, lots of options, I found middle click via tapzones (top left/right act as middle click in my config). It's also larger and has less friction than the 311c trackpad.
Build quality is the same on both *books but the bigger screen on the 13z is more pleasing given that the resolution is the same on both.
I think that covers the bulk of it!