I think the issue is that you've interviewed two therapists with very different styles.

The "analytical" therapist is going to take the time to get to know you, let you take the lead, listen to you talk, and probably not offer a lot of feedback unless you specifically ask for it. It will take longer to see results and they'll probably be more subtle at first. This approach tends to be more of get to the root cause, analyze it and figure out how to change thought patterns to affect behavior changes.

The "cognitive" therapist is going to jump right in with skills and behavior modification ideas. This approach is all about "right now" results. It spends less time on the underlying issue, and is more about dealing with immediate behaviors and making changes to them. The therapist is usually more directive, and more solution focused.

So, I guess, the question is...what do you want out of therapy? That will lead you to the therapist that might be the best fit for you. Alternately, if you really like the first therapist, you could stick with her, but ask her if she could offer you some skills for dealing with things right now, and ask her if she could help to lead you in the conversations, as you're not sure what would be helpful to talk about.

For me, the relationship with the therapist is the most important thing. I can't work with someone I don't feel comfortable with. The therapist I have now, I'm very comfortable with, and trust strongly. Sometimes, I need more feedback than she usually gives, so I just tell her that.