Each business using Peershares will have their own blockchain that is independent of all others. Blockchains can be secured cheaply and easily using Peercoin’s proof-of-stake, once the initial (issuer-controlled) shares has been generated using proof-of-work.
I imagine the POW sidechain distribution can be fixed pretty quickly... Otherwise not sure what to think except it seems like a natural progression from ME in the long term. Might be too long-term to be worth the development overhead? I have no idea what I'm talking about.
IIRC the POW part is simply the generation of the genesis block, which immediately contains all the shares you intend to issue. Beyond that it's pure POS.
I'm not quite sure how it compares to ME, but they do have an advantage in being backed by an existing, major currency with a big market cap and decent liquidity.
I'm invested in both Peercoin and AGS/PTS, so I'm hoping both turn out great