What the the different applications and benefits of fist and open palm strikes?

Open hand travels faster. It can also access smaller spaces like the neck where a fist might not fit.

For a punch I prefer soft targets. Hurts less.

I think it is mostly personal preference and what you have been training. I prefer open hand not just for strikes but mainly because it lets me grab to go into arm bars and joint locks. Once you get past the hard hitting and get to the more advanced martial arts techniques an open hand is just simpler.

It will always come down to situation and application. A punch will be direct and powerful, a palm can be too. There is no 'best' or 'better', it really is all how you apply and what situation you're in.

Ex: chest

Fist - you can cause damage with the force, knuckles provide a way to dig into ribs/chest cavity/clavicle/collar bone, and the general force can cause knockback.

Open Palm - can create similarities as punch, minus the digging, but can provide a nice 'thump' and create shock if you aim for vitals (lungs/heart/sternum)

Ex: face/head

Fist - pretty obvious results. Fist + face = damage, bleeding, dislocation of jaw, disorientation, etc

Open Palm - can create similar results once more, but you may control it better if all you want to do is force your opponents head back to push them away and it can turn into a neck grab if necessary. You also now have a greater surface which to strike with (think a powerful chop/slap or striking while cupping the hands around the ears to create vertigo).

Again, this is just the tip of the iceberg to practical applications. In general, the fist will create a more solid, direct force while an open palm gives you variety of both force and versatility.

Open hand strikes give you versatility. You can palm, chop, you can go straight into a grab, you can use your fingers to dig, pinch, scratch gouge, etc. You also minimize damage to your hand.

Punching with the closed fist is very effective, as long as you keep your fist tight, your wrist stable, and you select the proper targets, but you limit yourself to either punching with the knuckles, throwing a hammer-fist, and possibly using the knuckle to rake or dig into pressure points.

Palm is safer than fist because less small bones are involved. Palm has large surface area which lessens external damage and has a danger of becoming a push than a strike. Fist has smaller surface area so it does external and internal damage and it’s more likely to cause a cut. Fist gives you about two extra inches of reach when compared to a palm strike. Overall fist is just better than palm, but it’s more prone to damage. With hard curved targets which has higher risk of damaged hand go with the palm. With soft targets go with the fist. With hard flat targets like high ribcage I think fist should be okay.

Some styles such as Uechi use few closed handed techniques. The benefit of the open handed technique is speed as others have said and the fact they can be lethal or inflict massive damage . The problem is that if you don't have highly conditioned hands the chance of hurting yourself is high.

The benefit of closed fisted punches is that they are easy to do. But they don't deliver the impact of an open handed, a shoken, or a haraken one.

Using open hand is less likely to result in you injuring your own hand or wrist is the main difference

after that its academic