The best cool box we ever had was one I made from a polystyrene box covered in foil as an emergency one. We kept it cool with a 5l bottle of water which we froze beforehand. It kept everything cold for a 3 day trip where the temperatures were high 20's / low 30's. The water was still partly frozen at the end.
All the people with electric ones were fine until their cars needed jump starting because the batteries were drained. People with the Tesco type cool boxes ended up with off milk because they weren't big enough to put enough of ice in to keep them cool for long enough.
If you get an electric one then either don't run it once you've camped (ie only run it on the way there) and just use conventional freezer blocks which you can often refreeze at the campsite, or else get a converter so that you can run it off the electric hookup at your pitch. Of course you'd need to book a pitch with electric.
When we first started camping we didn't bother getting electric hookup, but we do now. Yes, things stay frozen even without power, but butter and milk go off nonetheless, especially if you're opening the box several times a day.
We have an ordinary coolbox (albeit a very large one), and the campsite we stay at has a freezer that campers can re-freeze ice-packs in, so we take about 16 and always have 8 in the box and 8 in the freezer and rotate them twice a day, it keeps everything perfectly cold, and I have even kept meat in it with no problems.
Lots of campsites offer this service, so it's worth checking.