I used to have the EMM Labs CDSA SE until I upgraded to the Puccini with U-clock. I have not heard the Wadia, so I cannot pass judgment. Comparing the Puccini with U-clock combo(all further comments refer to this combo and not just the Puccini alone, feeding Bryston 28B SST monoblocks directly via its digital pre-amp) vs. the EMM player is like removing a wall, not just a veil, between you and the music.
The first things I notice about the Puccini is the enhanced clarity, truth of timbre, transparency and resolution compared to the EMM. The next amazing thing is the way the Puccini develops air and space around instruments to give a wide, deep and layered soundstage that is not artificially stretched but rather true to the actual positioning of the instruments. For example, the highs and lows of a piano does not stretch all the way from left to right but are imaged solidly where the piano is positioned in the stage, whether the piano is dead centre, left or right of centre, upfront or further back in the stage. The EMM is the anti-thesis of all that has just been described for the Puccini.