Provided the Axis is working properly, with the original power supply, and the arm is in good shape, and if all other factors are equal then yes, it will be more musically informative than the Rega. What you end up with in practice could be very different though... The Rega is famously consistent in SQ across decades of use. I wouldn't make such claims about the Axis.
If the Axis is not a gift, then I would try before you buy.
The power supply is especially crucial in this case because the design was tuned to the suspension 'pods' as well as the custom motor (not the same as the LP12 motor despite external appearances).
Having the board serviced --properly-- at a reasonable price is a challenge. And if it's not done right, sound quality and reliability will suffer.
Meanwhile, my experiments with a substitute PS (an excellent quality, electronic type popular for the LP12) were not satisfactory (sound was 'okay' but not great). The devil is in the detail, as they say.
The Axis came with the LVX, LVX+ or Akito mk1 and all had issues, so I would look at that too.
BTW, you might also consider the Rega 24volt (AC) kit for your existing turntable.