Can someone elaborate on this answer? Jim's post is no more meaningful to me than if he had said "Number 1 vs Number 2 trajectories."
First hit on Google with "mars type 1 2 trajectories":
http://www2.jpl.nasa.gov/basics/bsf4-1.php
The two short sentences about it on that page are only minimally enlightening, although I have found a little more, including some discussion in the context of Venus windows here:
http://www.mentallandscape.com/V_VenusMissions.htmFrom a practical standpoint, I gather the two trajectory types arise because there isn't actually a single ideal Hohman transfer orbit for multibody systems with varying inclinations. If you look at a porkchop plot (basically a graph of the characteristic energy (C3) required to make a transfer, graphed as launch date versus arrival date, with C3 shown by contour lines, colors, or a third dimension) you see two zones of minimal transfer energy. These aren't necessarily equal, but they do define two distinct opportunities.
Wikipedia has a more relevant plot from the 2005 window used by Mars Reconnaissance Orbiter
http://en.wikipedia.org/wiki/Porkchop_plotBlue contours are characteristic energy. Red lines are transfer times.
The minima on the lower left is the type 1 trajectory. If you view it full size so you can see the numbers, you will notice it is faster, but takes a hair more energy.
A related question I haven't found an answer to yet is if it is always the case that type 2 is more efficient?
Time is an obvious a reason to choose a type 1 trajectory (idle science teams cost money, hardware ages and experiences cosmic ray exposure, radioactive isotopes decay, etc). However, you also sacrifice mass, so I'm led to wonder if, for example, orbital missions may tend to more greatly benefit from a type 2 trajectory than direct entry missions.
* Edited - fixed first link