Having just gone through this myself on my new bike, I'd venture to say that if your hands and wrists are hurting that much, there's something in your set up that needs to be addressed. Gel padding is likely not going to fix it. It could be how your weight is distributed between front and back and/or the bars themselves and how they are positioned (tilt, stem angle and length, and spacers).

Have you had a professional fitting? I will tell you that I tried to tweak just about everything I could think of in an effort to relieve my pain. I wasn't getting a whole lot of guidance from my regular fitter so I finally made an appointment with another fitter who specializes in biomechanics. I'd already swapped my bars from the FSA Compact Wing Pros that I'd originally selected for the bike for the Dedas that had been on my old Bianchi. After putting me through a battery of exercies, he also changed my spacers and stem--both length and rise. In my case, my upper body was too cramped and it was making me all kinds of uncomfortable. It would have seemed that simply lengthing my stem would have fixed it, but it wasn't quite as straightforward as that. I had to come both up and out.

So, as a starting place, you might want to identify what's different between your bikes' respective geometries to see if that provides some guidance as to why one is comfortable and one isn't.