Right now it's looking like the Linux 3.8 kernel will be used for Ubuntu 13.04 since it will be released likely in mid-March, just one month ahead of the 13.04 release. With Ubuntu 13.04 not being a Long Term Support cycle, this is what the Ubuntu kernel developers believe will be their best bet. In terms of other fundamental kernel changes or new flavors, there aren't likely to be any except for PowerPC possibly coming back to Ubuntu.
On the ARM side, a single kernel supporting multiple ARM SoCs should benefit the 13.04 cycle. The improvements to be found in Linux 3.8 over the Linux 3.5 kernel in Ubuntu 12.10 are covered in Interesting Features For The Linux 3.6 Kernel, The Most Interesting Features Of The Linux 3.7 Kernel, and Features On The Horizon For The Linux 3.8 Kernel.
Supporting the Linux x32 ABI was also talked about for Ubuntu 13.04. They may enable the kernel support for Linux x32 in their 13.04 kernel while they already have the x32-supportive GCC 4.7 and glibc 2.16 within the Ubuntu repository. However, there's no plans right now to continue with x32 user-space changes for this next release. Right now it's up in the air if/when an Ubuntu x32 flavor will appear.