Shadow Bolt:
+ Better spell damage bonus due to its higher base cast time.
+ Benefits from sustained attacks over time due to Imp. Shadowbolt talent.
+ Doesn't require any other spell before it to deal its real "full" damage.
+ Very few creatures seem to be immune to shadow (though many resist it).
- Mana-intensive to spam, requires either frequent drinking or plenty of Lifetap and Dark Pact.
- No other spells have true synergy with it other shadow "nukes" help only indirectly and only with the improved shadow bolt talent.
Incinerate:
+ Quicker Base cast time. If you don't have 5/5 Bane, this will be faster than your Shadowbolt.
+ Great synergy with fire spells. Immolate, Incinerate, Conflagrate all work together and can provide wonderful damage in the short term.
+ Much cheaper than Shadow Bolt of a comparable level.
- You *NEED* to immolate the target first to get your full damage out of it.
- Damage bonus from gear will not be quite as high as Shadow Bolt.
- Does not benefit from sustained attacks like Shadow Bolt does.
- Quite possibly the most God-awful slow spell animation I have ever seen. It swerves like a drunken sailor and feels like it takes forever to land (though it could just be aesthetic, I haven't tested which is actually faster).
Basically, Shadow is the way to go for the long run. It's a no-brainer with spells like Corruption, CoA, etc that it is intended to benefit the most from continued pressure~ chipping away at the enemy with DoT and blasting away with Shadow Bolts that get better the more of them you cast! It takes more time to set up, but provides very high sustained damage.
Fire is better for the "short sprint" kind of fights. Fire spells tend to rely on a fast-paced volley of fel fire. Immolate runs its course quickly, but is a hybrid DoT due to its substantial front-loaded damage. This is the more efficient choice for short, intense fights as it produces a good damage/mana ratio that is stronger in the short than the long term.
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Bottom line:
I use this to take out the trash. I'm usually shadow-oriented, but it doesn't make a whole lot of sense to use my DoT spells on something that will die most likely half way through. They're mana-efficient spells, but not so mana efficient that I feel I can justify "wasting" half of them. An incinerate is a nice opener (especially since it can hit rather hard if you have Ruin), and you're guaranteed about 1/3 of your damage with it as soon as it lands. Beyond that, it only makes sense to incinerate away, as it's cheaper and you won't be able to milk an improved shadow bolt for what it's really worth anyway.
If I were destruction-based, this could very well rival shadowbolt as my primary spell due to the very nice immo-incin-conflag cycle.
I think it was mostly added because fire-locks didn't have a nice staple nuke. It should however not be neglected by other warlocks, as it can if nothing else provide a mana-efficient way to burninate your way through the trash to get to the mobs you really want to demonstrate your shadow mastery over.