Like many people (especially those who live in cities) I have many ways to commute home.

Which type of route do you prefer (and why?)

Your poll doesn't take into account the variables I use. If I have a bike friendly route that has wide, clean shoulders then I pick that one. If I have 2 equally friendly routes but their is a speed difference, I pick the slower route. If I have a route with 2+ lanes in each direction or a regular 2 lane roade, I'll pick the 2 lane road. Even though logic dictates that the 2+ lanes should be easier to get around me, people tend to be less patient on those types of roads. I don't like weaving through neighborhoods even though those are the least traveled streets. It's usually too indirect and their are kids that think they can run out in front of you.

What about fast along empty side streets?

Or fast through the park or cemetery to avoid busy streets?

Or the days I want some extra miles and take the long loop?

I chose fast, but the real answer is both. I like to ride fast most of the time, but sometimes I might be tired and just want to cruise at a slower pace and not worry about fast moving traffic, so those days i'll take the back roads.

I like a variety.

I consider backroads (residential streets) safer -while not always necessarily slower. For me safety is the overriding criterion.

Both. Sometimes I feel like putting the hammer down, sometimes I feel like taking it easy.

When I'm late I'll often take the shortest-path route, but I prefer to take a longer, less-busy route. One benefit of bicycle-commuting is stress-relief, and this is greatly abated when taking stressful busy streets.

I like going fast along slow back roads. Fast for me is nowhere near fast for a car

I take the routes with the bike lanes. There are no back roads in Manhattan. The only consolation is that I get to ride in Prospect Park for a short distance.