Did a bit of research thinking that the Yetis might use some new sort of foam inside them that has a higher R-Value, but they don't.
Their secret is that they use really thick foam, it is hard to beat extruded polystyrene (think the house insulation sheets that Lowe's sells), this stuff is used in contact with ground so it does not absorb water. The thing that was new with the Yeti coolers was how the plastic is formed, they use a process called rotomolding that allows some really good and heavy plastic molding. Yeti insulates the lid also, most cheap coolers don't have an insulated lid, just double walled plastic, they also put a good seal between the lid and body and some latches that hold the lid tight. Where they differentiate themselves is you can beat the absolute #### out of the cooler, they are bear resistant if you put a padlock on them. Personally if a bear is in my camp I don't mind if it eats my food nearly as much as if it trys to eat me.
A cheap stryrofoam shipping cooler that has 2 inch thick walls and lid will keep ice just as well as the yeti, just won't be all that durable.
One neat thing I saw was someone that took a cheap cooler and was able to get three of these styrofoam coolers to fit into their plastic cooler perfectly. They used one for frozen stuff, another for non frozen food such as meat, cheese, potato salad etc, and the third for drinks. They took a container and filled it with ice and put in the bottom of each styrofoam cooler so when the ice melted it didnt get their stuff wet, then they filled the voids left in their cheap plastic cooler with ice. The ice just in the cheap plastic cooler melted in a day or two but the ice in the styrofoam coolers lasted a week.
Anyway if you are looking for a better cooler than the $20 igloo or coleman you can try the Coleman Xtreme series those have insulated lids, or you can bump it up a bit and get the Igloo BMX series that use a different molding process to achieve a cooler similar to the Yeti style coolers.
Here is a nice Coleman for about $50
https://www.walmart.com/ip/Coleman-52-Quart-Extreme-Cooler-Blue/21721549
Here is a nice Igloo for about $80
https://www.target.com/p/igloo-bmx-52-quart-cooler-white/-/A-53157099
