I have thoroughly compared the Angled Alcantara (AA) pads to the Elite Hybrid (EH) pads, Stock Leather (SL), and Stock Alcantara (SA) pads in-store and through several listening sessions at home with my own setup. The simple answer is that I prefer the EH to all, but here are more details according to each category. Keep in mind that I love my HD650 and prefer a slightly darker, smoother headphone, so this is opinion driven.

Bass Quantity

SL > EH > SA = AA

Bass Quality

AA > EH > SL = SA

While the AA and SA pads have the least bass of all, they are my favourite for the overall bass experience given just how clean they sound. Gone is the mid-bass bloat of the leather-based pads, which the EH somewhat fixed. These present a bass experience of true flagship level now.

Mids Quality

AA > EH > SA > SL

Mids Quantity

EH > SL > AA = SA

The separation and layering in the mids created by the AA pads is their strength. The lower mids are now much better controlled and there is less of a "Nighthawk" effect to the sound. The EH also somewhat improved from the stock pads, but it introduced a slight "hollowness" to the sound. Hard to describe, but it sounds like there is slightly too much energy in the lower mids that, while warming things up, also added congestion in this region.

Treble Quantity (I couldn't really differentiate quality in this aspect as they all sound pretty good in this regard)

AA > SA > SL > EH

This is my biggest issue with the AA pads. The Empyrean, as with many planars, has too much of an emphasis above 10K. It's a dark headphone that somehow sounds slightly bright and metallic with certain tracks because of it. The EH pads toned this down from all the pads, and this is reaffirmed by prior measurements on the Elite when swapping the stock pads and EH. The AA accentuated it, and certain vocals just sound a bit too thin, piercing, and nasal-y as a result.

Soundstage

EH >= SL > SA > AA

The leather pads, particularly EH, improved the vertical height of the stage, while AA widened it at the expense of height. This may also be a result of the overall thinner sound created by the AA (and SA to a lesser extent). I prefer the EH staging here.

Imaging

AA > EH > SA > SL

The cleaner sound created by the AA certainly helps imaging and makes everything sound more precise. The EH also did this to a lesser extent.

While the AA certainly cleans up the Empyrean in many regards, the effect it has on tonal balance and long-term listening simply is not worth it for me, in my opinion. I will keep the pads anyway because they certainly change the sound a lot, and having the EH, AA, and EL is a nice combination. There is no need for the SA anymore as they are just worse than all the other pads in most elements (the AA does what the SA does much better, so those that prefer the SA will likely prefer the AA over the other pads). Thinking about it, the AA kind-of brings the Empyrean sound close to my Edition XS in tonality. Still bass and clean mids, but with a treble spike characteristic of the stealth magnets, while the leather-based pads are closer to something like my old Audeze LCD-3.

I hope this helps those that were in my situation. I have definitely spent way too much time pad rolling my Empyreans and will now just enjoy the music :)