I'll preface this in general terms; it may depend on where/ how you hunt.
If there is no snow and you pulling by hand, the carts are easier. If you hauling with an ATV then sleds are better regardless of snow or not, especially if your traversing water.
We tried a cart at camp one year..it failed miserably, mainly because most of our deer are shot in the bush and trying to haul them out over fallen tress and branches was just more work that it was worth. If you hunt fields and just need it to carry to the truck, the cart would work great.
I've used an Otter sled for years....it floats as most of the areas I hunt are wet. (see below).
https://i.imgur.com/DoWgZPLl.jpg