The two sentences have a slightly different meaning but both of them express equally that you still work at the company, but for different reasons. In the first it’s because of the words ‘since 2013’ and in the second it’s because of the words ‘I’ve been working’ The difference in meaning is that the first sentence talks about how your present situation is affected by past events. The second talks about your activity in the past. Examples: Are you an experienced employee now? Yes, I’ve worked here since 2013. What have you been doing in the recent past? I’ve been working here. Of course you can answer both questions with either of your sentences, but only in the examples above are the answers consistent with the focus of the question.

Both give the same meaning, as both sentences can only be used if you still work at the company. The difference is that the second sentence (present perfect continuous) puts more emphasis on the fact that you still work there

I would agree that both would be used in that context. Are they exactly the same? I wouldn't think so. Sentence 1 uses Present Perfect and Sentence 2 uses Present Perfect Continuous. That's similar but not exactly the same. Otherwise, why define the tense as slightly different in English grammar. 1 - a past event that has present consequences. "I have worked on this project for two years and I am sick of it. I quit!" (Past event, present consequence). 2- an activity that started at a particular time in the past and is still continuing up until now. "I have been working for the same company since 2015 and I have no complaints. (Started in the past and continues now). In my opinion, Number 2 is the better option given in your example.

They are the same. The word "have" (which makes the verb present perfect) indicates that you continue to work there.