Depends on what you are doing with the axle.
The 8.8 is a nice axle. I had one in my YJ
But, it has a huge drawback over the 44. Ground clearance. It is big and hangs down low. Much lower than the 44.
If you are just going 33 and maybe 35s ?
Do you wheel a lot where ground clearance is an issue? Diff dragging a lot? etc? Or mostly light wheeling, forest service road driving?
For wheeling, the 44 is the better way to go. For forest service road running and daily driving, the 8.8 is probably the better value install.