I don't know that I'd say someone is "more justified" for using a fallacious argument rather than using an unreliable method. And at least some people who promote logical arguments for God's existence point out that they themselves are actually convinced for other reasons (typically more along the lines of personal experiences). But anyway.
If our primary epistemological concern is to believe true things, then I'd argue we should stick to methods that can be shown to be reliable. That is to say, the method produces many conclusions that can be shown to be true and few (or no) conclusions that can be shown to be false. It also helps if different people can independently apply the method to the same data and reach the same conclusion.
It also helps if we can explain why the method is reliable, and when, how and why it isn't reliable in the cases where it fails.
If you consider "feeling something in your heart", pick 1000 theists who uses that, and you'd probably have 1001 incompatible conclusions about who God is and what he wants and so forth. This method leads to outright contradictory conclusions (God can't want A and not A at the same time), so we know a whole bunch of those conclusions must be false, and we don't know that any of them are true (unless you have some independent reliable means of discovering truths about God... in which case we should probably be talking about that instead). That's close to the worst-case scenario for reliability. If you expand this to intuition more broadly, you do get some true things, but you get a whole lot more false things, so we're not doing that much better.
If we compare this to something like science, you need only look at the room you're in right now and you'll no doubt see many things built on top of science, thanks to the reliability of its conclusions. You might struggle to find something science didn't have at least some part in, including like fruit.
* Although science models behaviour, and it's built on verification and falsification, rather than proof as such, which leads to some questions about how "true" science is, but that's another discussion.
We can also consider something like eyesight, which is generally fairly reliable, but we also know of cases where it fails, such as if you're particularly tired (or asleep, for that matter), if you're taking mind-altering substances, if you recently suffered a brain injury, if you have one of a handful of mental conditions, if you see something out of the corner of your eye, if it's dark, etc. And human memory is also fairly malleable. So we could try to corroborate that with other evidence to get to a more reliable method.
Abstract syllogisms also seem fairly unreliable, while we're on the subject. Theists look at an argument and think it's perfectly sound, while atheists point out a bunch of fallacies. Or we just disagree on premises. Logic is certainly a helpful tool - it can help us see problems in reasoning, but it's easy enough to wrap one's preconceptions into the argument, such that the reasoning looks proper to you, but not to someone who doesn't share those preconceptions. It's especially ineffective if one (or both) of the parties aren't all that open to changing their mind, so they aren't trying to see what's wrong with the argument as much as they're trying to use the argument to convince someone else.
If you want to be pedantic, you could point out that we can't definitively determine whether something is true, due to solipsism (we can only be completely sure of our own existence).
In response, one might bring up e.g. coherentism, where we build a coherent model of "truth" based on the evidence we have available (our sensory experiences). We could also consider predictive power, i.e. whether our conclusions lead to correct predictions, which could add confidence that the conclusions are true.