Is having a religion or not having one more good?

I'd say this question is one that has a category error.

There reason is because the question is about morality, and the categories do not have a direct mapping to it.

The nature of question rests upon the idea that religious people have a moral code to follow, while the non-religious do not. But the moral code of the religious can be problematic, and the non-religious may have a moral code of their own. As for the question of the existence of different moral codes, I'll kick that aside. That is because different perspectives exist, and there is no set of logical principles (and there never will be,  at least by my religion) to determine objective morals. So then, regarding the question, my answer is this:

Adherence to or Non-Adherence to a Religion is not an Indicator of Adherence to or Non-Adherence to a Moral Code.

Religion provides a moral code. But that does not mean those who claim to adher to a religion follows the same moral code. And at the same time, those who do not have a religion, may have their own moral codes. And some of those who adher to a religion's moral code could also be taking an interpretation of it that's worse than what it actually is based on their inclinations.

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Now which is better, to have a wrong moral code or to not have one at all? Note that this is different from the question of there being different moral codes. Now this is a question similar to the question of whether it is best to not know how to sing, or to know the wrong method of singing. Both involve practice, so we can use the concept of hysteresis (as in magnetism) to make sense of this. And on the other hand, those who are without a moral code are different based on their inclinations. Those who are inclined to do good are better than those who are inclined to be bad.

So then, those who have a good moral code are better than those who do not have a moral code, but are inclined to do good, and they are both better than those who have the wrong moral code, and they are better than those who do not have a moral code and are not inclined to do good. There can also be a neutral quality for those who are unsure. I see that this is similar to the alignment chart used in Dungeons and Dragons, that is, the ones with Lawful Good, Lawful Evil, Chaotic Good, Chaotic Evil, and the 5 Neutrals.

This ordering is based on the idea that a magnet polarized in the opposite direction will require more effort to be correctly polarized than a non-magnetic material. But someone that has no morals, but is inclined to evil is more like a magnet polarized in the opposite direction by free will, with no interest in correction, as opposed to the ones that are polarized in the wrong direction by accident. Is non-magnetizable materials an analogy for this? I guess this analogy does not map well here, but just provides a way for us to understand the difficulty of correcting people. It's not even that big of a deal, but I just like to think mathematically in all cases.

Now the direction of polarization as I mentioned here, by which one judges whether a given moral code or inclination is good or bad, is subjective to each person, based on their morals. That is as I stated above, a reality that is not a problem in order to be solved. What each person must do is to live according to their morals, and strive to make the world in their image, and the rest is up to God.