You say that:
I argued that since science hasn't given a proof of the existence of God there is no reason to believe in it
You are assuming that there is a process by which an idea could be shown to be true or probably true: justification. As Popper pointed out in Chapter I of "Realism and the Aim of Science" justification is impossible, unnecessary and undesirable. If you assess ideas using argument then the arguments have premises and rules of inference and the result of the argument may not be true (or probably true) if the premises and rules of inference are false. You might try to solve this by coming up with a new argument that proves the premises and rules of inference but then you have the same problem with those premises and rules of inference. You might say that some stuff is indubitably true (or probably true), and you can use that as a foundation. But that just means you have cut off a possible avenue of intellectual progress since the foundation can't be explained in terms of anything deeper. And in any case there is nothing that can fill that role. Sense experience won't work since you can misinterpret information from your sense organs, e.g. - optical illusions. Sense organs also fail to record lots of stuff that does exist, e.g. - neutrinos. Scientific instruments aren't infallible either since you can make mistakes in setting them up, in interpreting information from them and so on.
We don't create knowledge (useful or explanatory information) by showing stuff is true or probably true for reasons so how do we create knowledge? We can only create knowledge by finding mistakes in our current ideas and correcting them piecemeal. You notice a problem with your current ideas, propose solutions, criticise the solutions until only one is left and then find a new problem. We shouldn't say that a theory is false because it hasn't been proven because this applies to all theories. Rather, we should look at what problems it aims to solve and ask whether it solves them. We should look at whether it is compatible with other current knowledge and if not try to figure out the best solution. Should the new idea be discarded or the old idea or can some variant of both solve the problem?
A more accurate criticism of the idea of God would point out that it doesn't solve any problems. If God made the laws of morality or science or whatever a particular way for some reason, then any physical mechanism that respects that principle would explain the same phenomenon. For example, if God made organisms to keep their genes in existence, then evolution explains their behaviour better than God. And if God had no reason for making the world behave a particular way then we might as well say "shit happens" rather than go to the trouble of postulating God. So God's existence solves no problems. And since God introduces lots of problems, like the problem of evil, the idea should be ditched.
Your friend claims that he feels God in his heart. Harry Potter fans may feel good when they think about him, but they don't feel the need to say he really exists. You friend should not need to postulate the existence of God to explain his warm and fuzzy feelings. And whatever your friend likes about the God story, he can still like it after ditching belief in God, provided there is no argument against liking it.
You ask if science is better than personal belief. It is better to have the idea that all of your ideas should be open to question. On issues where ideas can be experimentally tested, it is better to want to do the tests, so you can eliminate bad ideas. But there are issues where such tests are not possible, such as the question "Should ideas be experimentally tested where possible?" That issue can't be decided by an experimental test because any such test would presuppose that you ought to do the test. So there are issues that science can't resolve and some other way is needed to decide them. If the issue is "should I eat some ice cream?", then your personal preference that you should eat some ice cream would be more relevant than scientific knowledge about how to make ice cream.