Nuance between to have experienced something vs to have had an experience of something

Friend: have you ever dated a cop girl?

Me: Nope

Friend: I have had that experience/ I've experienced that.

I know to have had an experience of something is a rather broader statement than having done something.

It expresses that the person has been through the sequence of events that is typical when dating a police officer.

But can I use ' I've experienced that' instead of ' I've had that experience' here.

Would they mean the same thing?

• I have had that experience
• I've experienced that.

To me, there is a great deal of overlap in the meaning of those two sentences, so they could be or even often would be used to mean the same thing, but I do see the possibility of nuance there.

For me, saying "I have had that experience" potentially casts the experience further away from the speaker, like the speaker isn't fully embracing the experience or is treating it like it was something that was inflicted upon them instead of something that they themselves engaged in and did, possibly even dodging some personal responsibility.

So, were I to hear "I have had that experience," I would more likely infer that the experience may have been unpleasant or negative or something the speaker didn't fully want to own up to, so my response to them would become more likely to tread lightly to explore those avenues than if I were to hear "I've experienced that." Since "I've experienced that" isn't completely devoid of its own ominousness, my response to that, depending on their tone, might jump off with some similar exploration, albeit probably a less hesitant exploration on my part since the speaker is clearly owning their actions there.