They aren't identical, not like some models where they re-certify the exact same model with no changes, but the design is fairly similar so I don't think they changed very much to get it to pass.
Some people have said the headrest doesn't go up as high on the R129 one. You also have a standing height limit of 105cm on the R129 version (but people were saying it's outgrown before this anyway) whereas the R44 one you can use up to 18kg as long as the child's eyes are no higher than the top of the seat.
The belt routing has a slight difference in the R129 in that the extra hook for rear facing is also used in the forward facing routing. I don't think it actually does anything, it is just because under R129 you can't have different belt routings for RF/FF, they have to be the same. It's possible that it adds an extra bit of protection against forward rotation but I think likely not a huge difference.
Because R129 is stricter on side impact and the forward movement tolerance is stricter it's possible that the R129 one performs a bit better, but it's impossible to tell because there's no direct crash test comparing them.
The R129 one does advertise memory foam in the headrest whereas the R44 one doesn't, but the Graco Extend R129 (which seems to be the same/very close) doesn't have memory foam, so I don't think it will be that the old one doesn't meet the R129 side impact standard.
If you're wondering if you should upgrade, I wouldn't personally. I don't think the difference is likely to be that much. If you have a spare £130 and want to change your car seat, you get a bigger jump in safety by going for the Joie Spin 360 / Graco Turn2Me, because they have a support leg.