Brainwavz B2 vs MEElectronics A161p
Please note I don't have an extensive classical collection. So that part will be left up to someone else. Everything else I can do.
Bass
They both have a very similar presentation with the low end. The A161ps seem to do a better job digging into the sub-bass for bass guitars as well as much better texturing. Both offer great impact overall, they are just about at the same level actually. The A161, as stated does a better job as you go deeper. Neither is really tighter than the other though and the A161s have a slightly better punch, you'd have to AB to figure this one out though. A161 takes this one slightly
Mids
The A161s are sweeter than the B2s. Although the B2s offer a good amount of sweetness, the A161s do it more. Lower, distortion guitars are better rendered by the B2s simply due to the speed and precision in the midrange. That said, the B2s have better lower-midrange detailing while the A161s do as good of a job with the higher mids. Detailing and clarity are basically good throughout for the B2 and A161. Both offer plenty of energy in the midrange. At the technical level, the B2 and the MEEs are tied when it comes to midrange really.
Highs
In the high end, the MEEs roll off way too early, which is better than the more aggressive approach the B2s take. Although at this point, they both have a good amount of aggression to them. The MEEs do a better job with snare snaps while the B2s do an absolutely beautiful job rendering cymbal splashes. Although both IEMs do an ample job at sparkle and energy overall. Detailing and clarity, however, is a no brainer as the B2s are instantly miles ahead (not literally I guess) compared to the A161s. The roll off on the A161 can cause smearing on my end, maybe a bit of sibilance as well. B2s take this by a long shot.
Specifics
You asked specifically about clarity, sound stage (and instrument separation), as well as PRAT. They are below.
Clarity
Both have extremely great clarity to them. If I had to choose, the MEEs seem to offer better clarity overall compared to the B2s which only beat it out when you go to the lower mids. That's about it. Vocal clarity as well as higher instrumentals are taken by the MEEs. Clarity in the high end is definitely the B2s strong spot while the low end (not clarity, but presence) is better done by the MEE. It's really just a toss up.
Instrument Separation and Soundstage
Sound stage is about the same for both. Maybe slightly better with the MEE. Slightly as in barely larger. You're going to get a similar size, but different instruments pushed back and different instruments forward.
PRAT
The B2s get this by a long shot. They are simply faster and quicker than the MEEs. Midrange guitars, snares, as well as drums in general are a lot faster. This is due to the quicker decay of the B2s which is naturally done. MEE decays a lot slower, but as dynamic (in different areas though).
These two IEMs, in my eyes, are at around the same level. The B2s do sound more refined due to the high end and its speed and precision though. The MEEs dig deeper and take on a sweeter sound (which can lead to better perceived clarity).
Hope this helps. Let me know if you need any clarification on anything (it's midnight right now

).