The other night when I logged on things were pretty quiet in the militia so I decided to do some plexing in a nearby system to get a feel for the rewards and efforts.
I started using a Thrasher in a Minor plex, earning 10,000 Loyalty Points (LPs) after running down the ten minute timer on the objective (aka the button). My destroyer was setup for PvP so not ideal for this type of work, but it sufficed.
Next I tried a medium plex using a Wolf assault ship (also PvP setup). The button required 15 minutes but too longer because I had to close with my targets to deal damage which took my out of range a few times, but the Tech II frigate had no troubles tanking the NPCs. That got me 17,500 LPs.
Finally I went to base and grabbed a Cerberus Heavy Assault Ship (sort of half and half PvP/PvE setup that I made up from a scramble CTA years with spare parts found in a NC station) and ran a gated Major plex in the same system. The button required 20 minutes of controlled but the long range of the HAC made it easy to kill the NPCs and stay and range. Earned 25,000 LPs.
Each of the plexes raised my standings with the Federal Defense Union by 0.63%, and moved contested state from ~15% to ~19%.
I can definitely see why minor plexes are the preferred ones: requires less risk because you are using smaller cheaper ships and opposing ships have to be limited to similar smaller ships, and if you are interrupted you lose less time if you have to flee just before completing the plex (i.e. get driven out after 19 minutes of plexing, you lose a whole Major plex but only one of two Minor plexes).