I think it's true that the first one sounds more general. It doesn't /have/ to be more general, but I would probably interpret it that way.
When you say "what it's like to go out with her," it sounds like you mean "what it's like for EVERYONE who goes out with her." You're describing something actual ("is"), so you're wondering what it is actually like for the people who really do go out with her. You could also be wondering what it's like for one specific person to go out with her (for example, her current boyfriend), but without any specific context, it sounds like you just wonder what it's like for people who go out with her, in general.
In the second version, with "would," the hypothetical seems to imply that you're wondering what it would be like for YOU to go out with her. It's also possible that you could mean "what would it be like for someone/anyone/people in general" to go out with her. But it seems more likely that you're speculating about what your own experience "would" be like.