There is a difference between DP+ and DP++. DP+ uses external level shifter, DP++ uses passive adapter and the card switches different transmitter into the path internally.
> I think it was not completely passive, but simple level conversion; DisplayPort is AC-coupled signal, HDMI is DC-coupled.
Wait, I don't think that's accurate. I've worked with HDMI/DVI and both are AC-coupled, that is, you put a 10 or 20 nF cap in series on the TMDS lines if you're driving directly from an FPGA's digital IO pins.