A folio case is something that you leave on your Surface the entire time. It is nice as you never have to worry about taking the Surface out of the case to use it and the unit is protected all the time. Folio cases do have a few cons in that they permanently add bulk and weight to the Surface and many of them don't completely close until you remove the Type Cover. Sleeves are just that: sleeves you put your Surface, Type Cover, Pen, and a few smaller accessories in. They often have more protection than folio cases, don't add weight to the Surface itself, and can often hold smaller accessories like a thumb drive or mini-DP to HDMI adapter. The only real con of sleeves are that they don't always protect your Surface. Take it out of the sleeve and it's no longer protected.
I relied on folio cases with my various iPads over the years but switches to sleeves when I purchased my Surface Pro 2 and now Surface 3. I prefer them simply because I'm not adding bulk to my tablets. Plus I think sleeves make for better travel companions in that they protect the Surface more while in a backpack or bag. I would often end up putting my iPads in a sleeve while keeping their folio cases on during travel, I would probably do the same with my Surface 3.