You'll get much better performance (e.g., insulating value) from a hard-shell cooler than a soft-shell. Soft shell coolers are primarily radiant heat reflectors, with little insulating value. I also find that they quickly develop leaks, making things messy when used with ice.
There are hard coolers that have great ice retention abilities. The Coleman XTreme 5-day and 6-day coolers, Engel DeepBlue and Yeti coolers are examples. Practical Sailor magazine did a comparison of large, high-end coolers in 2008. Engel won with the best ice retention time, Coleman Xtreme came in second, Yeti third. The Engel is also advertised as bear-proof when used with padlocks or carabiners on the corner hasps (hopefully, not a potential threat inside your car).
I keep a small 12V/DC Engel refrigerator in the back of the Jeep. It's over 4 years old now and has been to hell and back. Okay, not hell, but it has been to the remote mountains of Ecuador (as check-in luggage on commercial passenger flights, then bounced around in the back of pickup tucks and buses), high plains in Utah, and throughout the Rocky Mountains, which is close enough to hell. It still runs like a champ. The only problem is it will run the Jeep's battery flat if I don't use the Jeep for a couple of days with the fridge turned on.
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2010 Jeep JKU Rubicon | 35" KM2 & 4" Lift | Skids | Winch | Recovery Gear | More ...
'13 Wheeling: 8 Camping: 6 | "The trail was rated 5+ and our rigs were -1" -Evan@LIORClub