I am a long time cork handle lover and i have always just bought rods that had full cork handles.  I have recently, as an experiment had a rod built with a carbon handle and i feel like its a huge win.  Tons of grip even when wet, and holds heat while fishing.  When its cold it seems as though my rods and reels steel all the heat from my hands and i quickly loose feeling.  I have hopes that they will hold up well making them a total win.  The cork i love is becoming very expensive and the good quality stuff is harder to get.  If your a weight driven angler they are lighter than everything else.  From one angler to another give carbon a look and see if you like it...

I have been wanting to built a rod with a carbon fiber handle. They seem very nice. Currently in the research process as there are a few options such as buying a premade one or making the cores and skinning the grip your self. Either way it seems like carbon will be the way of the future as cork becomes more expensive. 

I like the carbon fiber handles on the Denali N2. I've also tried it on the Cashion but they didn't feel quite as tacky to me.

Winn Grip or cork for me. Have not tried carbon yet.

Loving the Winn grips on my Lew's rod. Cork would be my next favorite with EVA Foam being last on my list as it feels cheap and I hate when it gets nicks and gouges in it.

 

Haven't tried carbon fiber yet.

Making one's own cores is a big pain, so I buy the cores and turn my own cores to shape.  A drill press can be used with the addition of a base with a cheap ball bearing sized to a rod on which the core material is mounted and turned.  Clamp the base to the bed of the drill press to provide stability at the lower end, the rod goes from the chuck to the bearing.    I use 60 grit sandpaper, and the material is removed very quickly, so be careful not to take too much off.  For detailed directions consult this site:  https://rileyrods.com/home/composite-grip-store/how-tos/

 

I have purchased my cores from Riley, and admit that while I've never had troubles with them, others have found them "gone" at times.  there are other sources for the cores, but these directions are very good.  Suggest calling Riley if planning to purchase from them and find out if all is OK.

 

If you want the lightest, most sensitive grips possible, foam core is the way to go.  They also are striking in appearance, especially in the sun if finished smooth and glossy.  If you do like I do and have a butt knob, a front ramp, and a rear ramp, all three may be formed onto a single core, the cloth installed all at once, and then separated for use after finishing.  You will need to design the transitions properly with plenty of space between each element.