Argument from incredulity and God.

Fallacy as used by believers in God: There is no evidence against God, therefore God.
Fallacy as used by used by non believers in God: There is no evidence for God, therefore No God.

God can be the loosely defined as the prime mover, inteligent agent that put things in motion; a deistic God.
The way I see it the believers ARE presenting evidence for God but it is not considered ENOUGH evidence.
For example: Prime mover, Kalam argument, design and information systems found in life forms: DNA, cell metabolism and the evolution of consciousness.
Who is more entitled to say to the other side that they are committing this particular fallacy?
Is this a tie?

I believe this is an argument from ignorance, not incredulity. Both sides are asserting they are correct simply because the opposing side hasn't been demonstrated to be true. An argument from incredulity is when because someone can't or simply won't believe something, that the argument is untrue or unlikely, essentially.

My take would be neither are correct to say either is "more entitled" and both are incorrect reasoning. Each piece of evidence would have to weighed accordingly (I'm familiar with most of them though and iirc the premises of the Kalam do not lead you to the conclusion of God).

The claim of there being a God or there not being a God would require their own independent justifications, not just rely on the lack of justification for the opposing claim.

Hope this helps.

Let's break these down, starting with the atheist claim:

There is no evidence for God, therefore No God.

1) To say that there is "no" evidence for God is simply inaccurate. In both the legal and scientific domains, evidence evaluated based on it strength, which is ultimately subjective (unlike mathematical/logical "proofs"). It is far more accurate to say that one is not convinced by the evidence presented.

2) concluding the non-existence of something based on the lack of evidence for it is the argument from ignorance . One can only make an epistemic claim from the lack of evidence— that they don't believe that God exists .

Now the theist claim:

There is no evidence against God, therefore God.

1) We have the same problem with the claim of "no" evidence against God being an inaccurate claim.

2) Same argument from ignorance problem. But when it comes to belief...

3) There is an additional problem with this one. If we treated this like a scientific inquiry, then we would need evidence BEFORE we accepted the conclusion; we don't accept the conclusion (that God exists) simply because we have not found evidence against it. The evidence must support the conclusion for it to be accepted provisionally. However, in practice, we accept conclusions all the time without evidence, rather we simply trust the source. This is generally a good heuristic (depending on the sources), but when it comes to any important issue (like our eternity), we should ditch the heuristic and be more methodical in our approach.

Based on #3, I would say that the theistic statement is more fallacious.

"There is no evidence against God, therefore God" is the fallacy of the argument from ignorance - clearly. (And the existence of god here might be accepted pre-suppositionally.)

The burden of proof is on the one making the claim. God is a "huge" claim needing huge evidence. If they do not give a good argument, evidence or reason for the claim we have no reason to believe. In this case the non-believer is called an atheist: a provisional and agnostic position of not being convinced.
So it goes: "There is no evidence for God, therefore we will wait till you come up with something, until then no belief."
However others might be a nostic atheists - who claim to knowledge that god/s do not exist. I have not met many of these.