First of all, is there any difference between the two? They both seem to be islands with unbelievably hard enemies. What makes one heaven and the other hell?

Secondly, is there any way to give a character 100% immunity to all or most status ailments? Any other advice for dealing with these islands?

I don't know what makes one Island Hell and the other Heaven, But If you want to know the easiest ways to defeat the monsters, you can use Quistis' Degenerator to blow them away.

Isle to hell is more South and Isle to Heaven in North. North and South, Above and beneath; Heaven and hell. That has always been my thinking ;)
Except that I can't think why they should be different, just their locations I guess
Anyway, Have the commands recover and treatment on a party member if your on Hell, cuz of the Malboro's
Also have Blizzaga junctioned to elemental attack on both the islands and make sure you have meltdown with you ^_^
Other then that, make sure one party member with the treatment command is protected against sleep, beserk, confuse and any other status effect which may kill you....
Hope that helps you :) a risky way to defeat all quickly is too junction death or break to status attack... but if your party gets confused, you better hope for the best =D

<font color=red face="comic sans ms">Junctioning 100 Deaths to Status Attack is useful on the Island Closest To Hell as it affects Blue Dragons, Grendels and T-Rexaurs. Enemies on the Island Closest To Hell are generally easier to kill and give better rewards than enemies on the Island Closest To Heaven, so it is better to fight there. If you are going to put Death on status attack, also make sure that that character has 100% protection against Confuse.

I suggest two different strategies for fighting Malboros; both involve having Quistis in your party. Make sure that one charcater has a good status defence (put 100 Pains, Confuses, Breserks and Breaks on status defence) who will be able to heal the others. Use Aura on Quistis at the first possible oppurtunity and Degenerate the Malboro.

Alternatively, put Quistis in a critical status (yellow HP) and give her the Initative ability. She should hopefully get the first attack, which would be Degenerator. This works better if you set the ATB to Wait as you will have more time to select Degenerator. You will also be able to kill all enemies quite easily this way, as they won't be able to attack you while you're selecting your commands. ;)

The Island closest to hell has lots of different species of Dragons giving it the name hell. But the heaven i have no idea. i can not help much with the status just use pain and confuse in your def.

while on the subject of def you can get your team to absorb all elements. if u have elemental def x2 just junction 100 ultimas and 100 life magics to it. the only magic that hurts u is non-elemental (e.g. breath by Ruby Dragon)

One thing to note:

By juctioning 100 Death spells to status attack will not kill Red Dragons and Marlboros(I'm pretty sure about this). You might also have to hit the enemy more than once before it is instantly killed. But I still think Quistis' Degenerator is the safest bet.:)

Thanks everyone. :)