I have a couple of yetis, and use them pretty much daily for the last 3 years. Tough? Absolutely. Better than Engel? Not really. But still good. Mine get opened about 20 times a day, 200 days a year on average. The lid seals have held up great, the rubber closures have been replaced twice and are in need of replacement soon. While the tapered floor is cool for drainage, I would prefer a flat floor that you could stand bottled drinks on straight. Perfect drainage is not really something I need. A few other fishing guides here use the engels and they are holding up at least as good as my Yetis, so I see no downside to getting an engel.
Now as for ice retention, I am sure that it is fine for most uses, but hands down it is not as good as even a coleman cooler. I have camped all over south FL and carried my yetis side by side with igloo and coleman, and the yeti would not hold ice half as long as the cheeper coolers. I would pack the food in the yeti (and I do know how to prep and pack a cooler), which we would open 10% of the times we would open the drink coolers, and pack drinks and snacks in the colemans and the colemans would literally keep ice a full day or more longer than the yeti. Now there is no comparison when it comes to quality of construction, but based strictly on ice retention a $50 cooler whips my $350 yeti's ass handily. This is my biggest disappointment with the yeti. Bottom line, I have enjoyed the toughness of my yetis, and also the stability on the boat, but if I spend money to replace them I will most likely try another brand.