I think the two are hopelessly, forever entwined. There can not be one without the other. For me, I can not think of too many science experiments that do not involve numbers in some form or fashion. The very data of most experiments demand mathematics in some minute degree. Of course, I am no mathematician, but I would tend to think they probably feel the same way about science. It's sort of the age-old comparison, "without light, there is no dark; without good, there is no evil...".
Math, or specifically, Arithmetic, came first. Before anyone could experiment, or do anything what we would consider scientific, the concept and practice of counting had to be in place, maybe only enough to know that a hunter-gatherer had gathered enough nuts and berries for dinner, or there were enough awake to fend off some predator that might attack the tribe sleeping in the cave.
I think this is a really interesting, if somewhat philosophical and unanswerable question.
There are certainly valid arguments for the idea that math could not exist without science OR that science could not exist without math.
The fact is that what we need is a historical answer, that we just don't have. Did early humans begin counting and adding because of some scientific need? (food, hunting, movement of their tribes?) or did the ability to use math lead to the use of science? We can never know the true answer and as in most situations, the likely truth is somewhere in between. Science and math are clearly intertwined in a way that we cannot separate, becoming more and more so over time. Likely early humans needed basic math and science skills that they used together to survive.
I do not believe that there is a way to separate the two given their dependency upon each other. Math is reliant on science and science is reliant on math. I really think that this question is similar to the old adage: What came first, the chicken or the egg?
Sorry, but I think that this is simply a question which is unanswerable.