I’m not sure where I stand on the issue (that is, the persuasiveness of personal experiences as an argument for theism; I’m pretty confident about the existence of God). I’m keenly aware of the limitations of citing one's own subjective experience of a thing as a reason why someone else should accept the reality of that thing, and uneasy about putting too much store in such experiences.
I do, however, want to tentatively make the distinction mentioned above. When people think of religious experiences, they tend to think of an experience that is in some sense supernatural; a vision, perhaps, or a voice in one's head, some great flash of insight or knowledge that seems to have no earthly source. I am sure that such experiences do happen. Those who take seriously the metaphysical and historical claims of Christianity must in principle be open to the idea that God sometimes gives people a glimpse of a world or a reality outside this one, outside the normal world of thought and sensory experience.
These are the type of experiences I would call "mystical". Into this category we might put the Transfiguration, the first recorded mystical experience in Christian tradition; Augustine's "tolle, lege" moment; Aquinas' ecstasy while saying Mass that seems to have led him to halt work on the Summa; and the visions of Julian of Norwich. There are countless other examples throughout Christian history - though we must be cautious in our assessment, given what we now know about disorders and diseases which can give rise to hallucinatory episodes that might once have been regarded as religious experiences (the same applies, mutatis mutandis, to claims of miraculous happenings. While miracles can and do occur, not every occurrence described or perceived as miraculous is actually supernatural.)
There are many people, including friends of mine, whose faith is deeply grounded in, or has been bolstered by, profound mystical experiences of the divine. But equally there is a different kind of religious experience, which I suspect is more common. It is hard to describe in a way that does not make it sound trivial or banal, but I will try.
It is a deep sense of "rightness" - by which I don't mean personal vindication, but rather a feeling of having oriented oneself towards the way things ought to be, of having been in touch, briefly, with some underlying order or structure or pattern (hence I have a lot of time for Taoism). I get this sometimes when reading poetry - it's why TS Eliot resonates with me so deeply - or at Mass, or when listening to liturgical music. Now the sceptic will have a dozen materialist explanations to explain this, or some entirely plausible theory that I am just an aesthete with a bad case of wishful thinking. All I can say is that I have considered most of these counter-explanations and found them incomplete. And in any case, I am not primarily offering up these religious experiences as proofs, but simply as a demonstration that when we talk about religious experience we are not just talking about mysticism.