IMO a pair of 120qt coolers is the sweet spot, for a few reasons:
1. The 120qt size is nearly always available cheaply at local Walmarts/other stores. Sometimes you can find bigger. But you can (almost) always get these. If you have that coveted situation where you have both a bull and cow tag (it's a thing) you can show up with just 2 coolers at the trailhead but know that if you get really lucky, you'll be able to go double up cheaply.
2. Anything bigger than that is very hard to move once it's full of ice and elk. If you go bigger you need to think about the logistics of things like having to unload a carefully packed cooler you've kept in the shade for 2 days just to get it into your truck when you pack up to leave. Even a 120qt is a hug hassle - my friends think I'm crazy that I move it alone. But it can be done.
3. If you use a pair of coolers instead of a single one, you can keep one empty and one loaded with ice. If you get an elk down, you can scoop half the ice from the full one to the empty and it's the perfect amount. By keeping all your ice in a single cooler you have more thermal mass to keep the ice longer with less loss.
4. If you're like me and roll in with a truck camper in your bed, you're looking at cargo racks for the coolers. A single huge cooler full of elk AND ice will unbalance you, but if you spread it across two, it helps distribute your load.
5. You only need this much capacity for elk. Go out for pronghorn or deer? Just bring one cooler, and it's not insanely large for smaller game. Renting a pontoon boat? 120 is perfect for ice, drinks, food, etc for 4-8 people. Anything larger gets pretty insane.
YMMV - everyone has different needs. But that's what I roll with. Here's me all rigged out last season. Truck camper, two 120qt's on front and rear cargo carriers, valuable items like rifle/gear in the back seat. Notice that despite all the weight, I'm sitting fairly level and balanced. The front carrier also rides low enough with this cooler size to not obstruct my cooling. Obviously if you're tent camping just throw the coolers in your bed or the back of your SUV and they still fit fine - in that case my comments about being able to lift them when full apply even more, though.
