I (a Christian) am somewhat skeptical of the emotion-driven nature of those “born again” testimonies. I’m sure some people’s conversions really were that drastic (mine sort of was), but I also don’t like when churches/sects rely very heavily on such experiences and treat you like you’re not really a Christian if you didn’t experience such a drastic change. But those people are the minority, anyways.
In reality, being born again is not an “emotional” or drastic experience. All it is, really, is a change of heart or will from living in sin to living for God. It’s called “born again” because you are born as second time, in a sense, because in choosing God you inherit a new and eternal life with Him. There is terminology in the Bible, likening the experience to things like “stone turning into flesh” or “light breaking through the darkness”. And that is true; when a person chooses to live for God, His presence will cause them to become more like Him, making them more loving, kind, gentle, and desirous of the truth. But again, this is not meant to be a drastic, immediate incident but a gradual one that takes place over time.
Being too preoccupied with other things in the journey of life can spell disaster if you aren't watching where your going; some change lanes when they see the darkness of a tunnel, others when they hear the warning horn, some when they see the light, but most are so distracted for so long, they don't see the oncoming train until it's too late.
Going from agnostic to believer I wouldn't count as being born again, that is going specifically from being a non-believer, that is someone who disbelieves in God, to a believer.
A lot of believers don't share this but it's something I've observed in a few people that the faith isn't that strong. A lot of Christians I imagine are Christian in name only.
I think the problem I have with born again is the way people who describe themselves as such act, it all calls for a very grandiose view of things, beating one's chest or acting overly humble. It's too self-aware at the least, always getting in the way of itself. That's the problem with most defined phenomena, this overt self-awareness leading to a lessening of the thing itself.