A crude comparison of input delay between a PS2 ASCII Capcom vs SNK 2 Stick FT2 plugged into a Brook PS2 to PS3/PS4 Super Converter, and a PS3/PS4 Hori RAP V Hayabusa 2017 in one King of Fighters game each on PS3, PS4, and PC; I counted the frames between pressing the button for Kyo's light punch and his punch animation starting; the result was that the PS2 stick and Super Converter combo came out one frame slower than the PS3/PS4 Hori stick--which is not too bad, really.
You can play the video frame by frame by pausing it, then using the "." key to advance, or the "," key to rewind.
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Update 1/26/18 - In some cases at least the lag seems to be under one frame--in any case I've been running it with things like ACA NEOGEO games on PS4, and it doesn't appear to lose a full frame. So I guess I'd say that the delay is *at most* one frame.
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