Which is better?

I'm playing a variant of Deadrabbit's BM spark build (basically this with some alterations: https://mobalytics.gg/poe-2/profile/ed750a76-67df-4294-ba7c-6fa4b85d41ef/builds/eaaa3c6d-8967-4629-914c-69c266f1d53c

Given how damage is calculated, which wand is better?

Increased Spell damage + Extra cold dmg + Extra lightning dmg

or

Increased Spell damage + Increased Lightning damage + Extra lightning dmg

Here's an example of the wands. Which one would be better suited?

In general, "gain x damage as extra damage" is better. Its multiplicative, while "increased" is additive. The question is how you utilize different elements. Looking at that build (which is just generic BM spark, hardly deserving someones name on it), it doesnt rly get much from that cold and fire, so lightning wand might be better. But if you have sacred flame, extra fire/cold will be better.

You also didnt mentioned your alterations. Cuz if you heavily use warp, i would consider using Polcirkel for maping which could utilize that extra cold damage even without sacred flame.

Yes sir, I use the Sacred Flame, though it's possible I'll situationally pivot to a focus for more ES.

So with the Sacred flame the two "extra" fire/cold mods will be better?

Would you say that the lightning wand will be more versatile for alternating between Sacred Flame / Focus?