I would say that there's no such delay on the iPhone, either on the new model or earlier. Feedback to touch is instant, and dragging exhibits exactly the behavior you describe.
Are you kidding? The 3G has a very noticeable and annoying latency on input (e.g. when entering text, when switching between modes in the Maps app, or when switching between most apps). It's not the end of the world, but feedback is hardly "instant". Text input latency seems notably better with iPhone OS 3.0, happily.
Is there a phone which does A? The iPhone does A. Are you kidding, the iPhone doesn't do B!
The grandparent specifically asked about a 1/4 second delay on all touches, the iPhone is (at a guess) faster than 1/16 seconds, certainly well below the magic 1/10 of a second.
Switching apps on the 3G can certainly be sluggish, but is a very different problem, solved in part by upping the processing speed in the 3GS by 300MHz.