Which one of the following statements do you think is more appropriate? - You are being transferred. Your call is very important to us. - Hey Jane, I’m going to introduce you to our customer success specialist who will be better able to answer your question!

Probably the second option.

It would be more appropriate to apologize and thank the customer first for bringing his/her concern. Let the customer feel that as much as you want to help fix the issue, try to explain and ask the customer if is it okay if you're going to transfer his/her concern to a specialist since the issue is out of your expertise. 

Sometimes, some of the customers don't want to be transferred to another agent. If this happened, it is best way to listen and to understand his/her concern and then try to give options that would make the customer feel that you really want to help solve the issue even if it is out of your end.