The difference, in my opinion, is determined by experience using the plastic at all. Crystal Clear is an excellent plastic and is offered in 3 degrees of softness but it can have a learning curve. The Essential plastic is wayyyy more forgiving during the learn stages and is, again my opinion, far better to learn with.
The Crystal Clear soft formula need no softener at all. The Essential can use some softener if you feel as though a softer plastic is needed in smaller baits. The softener works in either plastic.
Heat Stabilizer helps make the plastic less likely to burn if gotten a few degrees too warm. The Essential plastic is more forgiving when it comes to cooking and will handle some higher temps without any stabilizer. The Crystal Clear products, as mentioned, have a learning curve that includes being able to closely monitor cooking temps and some stabilizer added to it can help eliminate problems but there is still a curve that only time and experience can provide. Should you decide either way, the stabilizers helps with heat issues in both of the plastics.
Nothing can replace a good digital thermometer like the one Do-It sells in their catalog. If you learn to use the thermometer religiously stabilizer can be nixed from the list of needs.
I make more small baits than large baits, primarily for panfish. I will soften the Essential on occasion making ice baits but I'm just as likely to use the Crystal Clear soft formula. I like both plastics. The Essential is by far the stronger, stretchier of the two plastics.