I have used many different rod covers. I in my mind, there's really only three different categories I have found to choose from, with some range of quality, price, features within each. All work, none are perfect.
1. Mesh. Usually nylon, I think. Think Rod Socks, Amazon no-names, etc. Cheapest choice usually. Biggest plus for me is that they dry quickly. Cons: hooks WILL get caught in the mesh at some point...whether in the car, or rod locker, or kayak...it is a PITA. The 'looser weave' (cheapest, generally) versions will allow you to poke a rod tip through the mesh, and will they do start to fray after a time. BPS and TW both have branded socks with a nice tight weave that are currently m the best choice for me.
2. Neoprene. Think Liv, 6th Sense, Rod Glove. Hooks don't get caught, tips don't poke through, best actual protection for the rod. More expensive and can be a bit more frustrating to put on (the ends fold over and you have to be a bit slower/more mindful; not a big deal to most, probably, but when you are stowing 10 or 12 rods at the end of a long day, they can be a bit trying). The real drawback for me is that these can take forever to dry. I tend to toss them in the bottom if the boat some times and if it rains before I put them away, it is guaranteed that I will stow rods with wet socks in the locker.
3. Fabric. Not sure if any commercially available, but I have had homemade versions that are pretty good. Used to be a variety on Etsy, FB, etc. Not sure anymore. The ones I had years ago were great. And, I contributed to a young entrepreneur saving for college. Of course the quality and price may vary widely here.
One problem I had with all of them is that they sink. Fast :). I see that Liv claims to float, and that is a good selling point.