The handle is the piece of the bat that you interact with when using it, so it's such a vital part to get right for yourself in terms of shape and size. In terms of the construction, then 3/4 piece, 6 piece, 12 piece, rubber, cork inserts. All the factors do tend to add up to achieve quite different feeling handles - but the most important is that it's well made and it's been well glued internally, as well as fitted correctly.
For myself, a handle with a solid feel, but with some flex has always been the style I prefer. I also prefer the handle to be oval, and probably more of a medium sized handle. I can just about get on with the Keeley handles, they are definitely on the skinnier side, but they do use a good quality stiffer handle, so you get a good blend of flex and stiffness despite them being a little skinny I feel. I just wrap an extra round of bind around any that are too thin, and they're just about okay then.
Then on the opposite side of the spectrum, you have ridiculously thick handles - which yes can balance well, but I've got an Aldred where the handle is something like 45mm by 40mm - it's actually probably detrimental to the feel IMO when you have a handle that's too thick - can feel it might slip out your hands. It may make the bat more balanced to the handle end, but because it's so thick it doesn't feel it sits comfortably in the hands, hence making the overall feel worse.
With regards to whip - it's something that I've heard Rob Pack and Julian Millichamp talk about in the way they've designed shapes, and you see players stepping on their handles to create that 'whip' in the handle. I think more a feel/control thing. Feel/control is definitely something linked to performance, as you have to feel comfortable with the shots you play and how you feel the ball off the bat.