Ok, tough to answer that question. Here are my impressions of the three parks. I am an intermediate rider (low end Cat2 if you need race terms).
None of those parks qualify as a fast flowy park. Each of those parks have fast or flowy sections.
Deer park - most approachable park. Simple layout and easy to find your way around. Climbing and some basic technical. the back section of white is as close to fast and flowy I can think of.
Stevens - The best Intermediate park. It has longer flowy sections but fast will be up to you. Large parts of the maze loop is specifically what I am talking about. I have never been to the "other side of the mountain" but based on the topo, if you can do the climbs you will get the fast.
Northern Allamuchy is really 2 parks (or 3 parks). The Sussex rail trail side offers some fast technical sections but not so flowy. The Tranquity side is much more technical and the fast comes on the way down.
Given that everyone will have different preceptions of these parks, my comments should draw out some disagreement (and useful information). However, this is how I see these parks.
Cheers,
"slow" Joe