I would recommend both. For many of the reasons listed. Even with pallet forks, there are some things it's easier or better to sling it and lift it with chains rather than trying to get forks under it. Especially if it's an oddly shaped or non symmetrical object. Or if it's too large to get the forks under it far enough. The ones that come readily to mind are lifting to move my 6' rotary mower, lifting and moving a neighbor's old pickup truck bed, and lifting the front of my riding mower to get the deck off of it.
I still use the pallet forks a bunch, even for non palleted stuff. But hooks welded on a bucket are super handy to have around.