Immolate - no affliction talent affects it.
Siphon Life - weak DoT, loses 50% of scaling due to being a leech.
Corruption - powerful DoT with lowered coefficient.
UA - powerful DoT, but weaker then corruption.
VS
SW:Pain - very powerful DoT, scales extremely well.
Vampiric Touch - powerful DoT, causes replenishment, scales well.
That's 4 DoTs for Locks, of which 2 are very weak, and 2 others weaker then both your DoTs.
In exceptional situations, we get a 5th, but it's very unlikely we will,
since Curse of Weakness, Curse of Recklessness and Curse of Elements have priority.
Now, another difference, you have 3 nukes, we have 2.
Shadowbolt - low power nuke that scales very well, gains a lot from spelldamage, evening out the low base damage -- crits for no extra damage
Haunt: average damage, low cast, doesn't scale too well, boosts damage of our DoTs -- crits for no extra damage
VS
Mind Flay(being changed to a nuke, currently a channeled DoT) - destined to be powerful -- speculated to crit for 60% more damage
Mind Blast - average damage, short cast nuke, doesn't scale too well, but causes a fair amount of damage on a low CD/Cast time, gains a lot from +dmg talents/effects -- crits for 60% more damage
SWeath - low to average damage, instant cast, doesn't scale too well either, but causes fair amount of damage at the cost of health, medium cooldown -- crits for 60% more damage
See, 2 different classes, with the changes, your DoT damage will be slightly lower then that of an affliction lock(not considering the changes that will happen to our DoTs since they're unknown for now).
Your direct damage, however, will be slightly higher, due to gaining more damage when you crit with your nukes.
overall:
Affliction locks will cause more DoT damage, but less direct damage.
Shadowpriests will cause less DoT damage, but more direct damage.
In the end, it evens out.