It really depends on what you mean by "stronger". Your question seems to be looking for a way to make two very different concepts of belief somehow comparable. There are a few ways to go about looking at that, but we first need to get clear on the two different versions of "belief" in your question.
You "believe" axioms for the sake of argument. Let's call this belief(1). You generally "believe" in God in a different way - you don't just accept God's existence for the sake of argument, you accept it as an impersonal reality. We'll call this belief(2). Belief(1) is systems dependent - when you move from Euclidean to non-Euclidean geometry, the axioms change. They haven't been falsified, but largely because you also never made a truth claim about them. You simply said that these assumptions look very reasonable and we need them to do interesting things with bearing on reality, so we'll treat them as though they were true, sidestepping altogether the question of whether they really are true.
Belief(2) is different. You don't just treat the claim as true for the purposes of doing something else. Belief(2) is an impersonal, systems independent truth claim. It's more impactful in that you're not just treating the belief as the foundation for an extended thought experiment. In some ways, this makes it more sturdy, in others, less.
Now, as I say, there are a few different ways of comparing these two to see which is stronger, and it depends what you mean by "stronger." I'll give three, but I don't claim this as an exhaustive listing by any stretch of the imagination.
First, we could consider the capacity of each for impact. In this respect, belief(2) is pretty clearly stronger than belief(1). Because belief(1) is systems dependent, it has no real facility to reach beyond the system into which it is bound. It has impact on the (intellectual) world only so long as its system is widely accepted. Belief (1) may give us new ways of looking at things, but it ultimately makes no claims about the way things really are. As such, it has relatively little power to change the world. This is not to say that its power to change is small, merely that by comparison to belief(2), belief(1) generally won't change as much as fast or for as long.
Closely tied to that first method of comparison is a second, the commitment each requires from adherents. Belief(1) is easily abandoned. Once the system to which it is tied falls out of favor or ceases to be useful for a current project, belief(1) can be left behind quickly and easily. Students learn to do this as their intellectual life gains complexity and they discover that principles which once seemed sure bedrock are actually more like sand traps.
Belief(2), by contrast, requires significant commitment. It requires more intellectual and moral investment, more time to create, and more time to destroy. It would be appropriately cognized, I think, under the name "worldview", in this respect, and many people have belief(2) about things like religion or politics. There's a reason civil discourse steers clear of those two items in the interests of remaining civil.
The contrast here may be nicely brought out by considering what it might look like to have belief(1) concerning one's political views. Consider, for instance, the explanation of a senior civil servant to a junior civil servant concerning the nature of his beliefs: "I have served eleven governments in the past thirty years. If I had believed in all their policies, I would have been passionately committed to keeping out of the Common Market, and passionately committed to going into it. I would have been utterly convinced of the rightness of nationalising steel. And of denationalising it. And renationalising it. On capital punishment, I'd have been a fervent retentionist and an ardent abolishionist. I would've been a Keynesian and a Friedmanite, a grammar school preserver and destroyer, a nationalisation freak and a privatisation maniac; but above all, I would have been a stark, staring, raving schizophrenic." (Yes, Minister, "The Whiskey Priest"). The senior civil servant very clearly holds his political views as belief(1) in the interests of being able to do his job. Most people are not so flexible.
The third way we might compare the two is in fallibility, and here, belief(1) shines. Because it's not making a truth claim at all, just presenting a hypothetical set of principles for the world to see what comes of it, belief(1) is basically unfalsifiable. Belief(2), on the other hand, is making a truth claim, and usually a very strong one. It therefore can be falsified. Belief(1) is the less prone to being wrong, but largely because it doesn't try to be right.
All of which is to say, you've asked a very complicated question to which no simple answer exists.