there is pdaXrom with 2.4.x kernel and pdaXrom with 2.6.x kernel
beta1 or beta3 is the latest stable release (depending on the model) using the 2.4.x kernel
starting beta4 and its successor r121, the kernel has been upgraded to 2.6.x
although the 2.6.x kernel is faster than 2.4.x kernel, some hardware support is not complete or missing, ie things that worked in beta1/beta3 which have a 2.4.x kernel, do not work in beta4/r121 anymore.
r121 is the current development path and work is being done to improve it and make it more stable. also, starting beta4, there is a new bootloader which renders NAND backups/restores inoperational (this will be fixed later but currently does not work)
since pdaXrom has moved to the 2.6 kernel and current work is on that branch, bugs in the older beta1/beta3 won't get fixed since all the bug fixes go into the latest release...
pdaXii13 is a branch based on the 2.4.20 kernel, ie beta3. it fixes a lot of bugs in beta3 hence pdaXii13 is equivalent to beta3+bug fixes. pdaXii13 also support the C3000 model which wasn't supported before. Tthe original intend for pdaXii13 was to support the C3000 only. later on, this has expanded to also support the C1000/C3x00 models because these models have the same base hardware and kernel as the C3000.