My explanation on why thunderlord is better than Deathfire on burst mages

For Vel'koz deathfire is going to do 3 + 10% AP in the early game. He doesn't get ~200 Ap till around the 25-30 minute mark (and that's if he's ahead). That means 30 minutes in the game you'll be dealing an extra 23 damage with each ability. It doesn't stack and simply refreshes. For Thunderlord you're getting 10 damage per level and 10% ap every 30 seconds. This means that in mid game you'll be dealing 120 damage every 30 seconds (20 after this patch) .

Deathfire takes 1.5s to fully do the 23 damage in the mid game. Vel'koz combo takes around ~3 seconds (ult included) meaning you'll land 46 additional damage. Your Q will pop every 4 seconds adding (if you can land it every time) another 23 every 4 seconds aka 138+46=184 every 30s (if you play perfectly) aka 64 more damage as burn instead of burst. This drops to 161 in a 20s time period aka 41 more damage.

You can't regen from the 120 burst, but you can for the 184/161. Looking at hpregen we'll see the difference. I'll use Koz as my example for regen. At lvl 10 he has 9.7/5 or 1.94s. 1.94x30=58.2, and x20=38.8 To calculate actual damage we'll take this away from the burn damage. Thus true numbers are 125.8/122.2 Compared to the 120 this doesn't look very good especially since Koz doesn't have very good Hp/5.

tl;dr They do about the same damage, but thunderlord is burst oriented (like the characters you put it on), and can't be countered as easily.