General

They all also have their own cool down time however when attempting to summon more then one at a time, the previous field will expire itself.

Purple Field: Usefull for mobing due to it's orb-bouncing-to-edge feature, since when it bounces to an edge, it attacks.

Light-Green Field: Usefull for bossing due to it's constant attack (usefull for HUGE size monsters).

Red Field: Boosts HP and avoid for you and party members inside the field.

I think that's the difference, i like this summon overall, pretty unique and is versatile.

For me, the purple field (force field) feels the most effective since it will usually bounce into the corner of the field which causes it to touch 2 times in close succession, whereas the blue field (penetrate) only hits them as it passes over them, so it feels like it gets less hits in. However, if there are a lot of enemies within the field then the blue field would be effective as it isn't limited to 8 monsters like the purple field and the blue field could constantly be hitting something if there are enough enemies.

The pink field (support) is pretty self explanatory though. It boosts the hp and avoid of party members that stand in the field and fills 1 bar in your power gauge (the gauge that is required to use certain moves and buffs) each time something misses and ally.

Reading the description goes a long way. Other than the obvious differences stated in the description alone, and assuming you're casting hypogram to deal additional damage; there are some key differences.
The purple field deals damage in bulk, at a slower rate, meaning that it hits higher per line, but slower compared to the blue field. The way the purple field deals damage is when the ball hits the top and bottom wall
The blue field hits rapidly, but is weaker in terms of damage per line. The way the blue field deals damage is when the little ball in the field hits the monster, so if the monster is directly in the centre of your field, it will get hit more often, vice versa when its along the edges -- it will barely get hit
Each have their benefits; I personally use the blue field for stationary bosses, knowing i could centre the field right where the boss is. I use purple field for everything else, for moving bosses and for training