I want to jump directly to the point; it really does not matter. Both cork and foam are excellent materials for fishing rods handles, and both can put up with years of abuse. I have been fishing for nearly more years than I can remember, and the rod handle material was never the reason I lost the fish or was the cause of a rod failing.
Both foam and cork work very well and really come down to personal preference. I like cork, it is natural, well mostly natural it is bind together with all types of epoxies and glue. but the cork itself comes from a tree and I personally prefer how it feels. Foam handles can feel a little fuzzy, kind of like velvet or peach hairs, just do not like that sensation. So, for that reason alone, I often avoid foam handles.
There is really not much difference in sensitivity between foam and cork fishing rods handle. Sensitivity comes from the blank, and if you want the ultimate in contact then touching the rod blank directly will give that. With that said, a thinner handle, will likely be more sensitive than a thick one. So for ultimate of sensitivity, you probably want one of those fancy carbon fiber handles. but it honestly does not matter. It is not going to result in any more fish caught.
On the matter of thickness, not all foam is created equal. More expensive rods typically come with a denser foam handle, which supposedly handles abuse better, but like I said in my opening paragraph. All my foam handles, on both expensive and cheap rods have survived the test of time.
I feel I must mention smell, I personally find foam handles, especially the cheap ones are more likely to trap unpleasant odors, such as fish blood and if frequently used they can become a bit smelly and even feel a bit slimily. Not really a big problem, just wash them, but thought it was worth mentioning.
Split or full grip fishing rod handles?
While discussing rod handles, I thought I will share my thoughts on full or split grip handles. I mostly consider it cosmetic, with split grip looking a more modern. But it is more than just looks. split grip rods are typically lighter than full grip. It is not by much, but a lighter rod is typically less tiring to fish with than a heavier one. So that’s one point for split grip.
Split grip also leaves more of the rod blank exposed, making the slightly vibrations of sensitivity easier to detect. It is a very slight difference, and most vibrations travel through the line, not the rod but I thought it was still worth mentioning.
Manufactures also seem to like split grip designs, critic in me suspects because they require less material. Meaning they are cheaper to assemble. Which means more profit or lower prices.
So far, I have only pointed out good points for split grips, but full length handles have a few advantages. Firstly, the extra cork or foam is rather buoyant, and it can be enough to prevent some rods from sinking. Not normally a consideration until you drop a rod overboard.
I also feel full length handles are a bit more durable when transported in rod holders. I have a few split grips where the rod blank ends up rubbing against the edge of the rod holder. While it has never happened, I always suspect all that rubbing could eventually compromise the blank which could cause it to break when the rod is under load. Although, that again is quite unlikely, because most of the rod load occurs above the reel, while rod holders typically hold rods beneath, the seat.
Summary
When it comes to rod handles, it really comes down to personal preference. There are some minor differences between cork and foam, but it really is not enough to matter.
It is a similar story with regards to split or full grip. It is mostly for cosmetic and I happily fish both sales and either will not prevent me from buying a rod.
More rod buying information
6 Best Spinning Rods For Trout Fishing (Based on real world use)