In general, peer tutors have the potential to be as effective as professional tutors or tutoring centers, however there are some forces working against them. First, by definition the tutor and student are peers; this very fact may hinder learning by offering a distraction from the material, either because of positive or negative social interaction. Depending on your student, this could serve to make the peer tutor more effective, based on a pre-existing relationship. Second, a peer tutor may have mastered the material enough to please the teacher or pass the class, but being able to teach the material to someone else demonstrates a much deeper understanding of the concepts than most instructors require. If you choose a peer tutor, make sure they have the added level of understanding needed to guide someone else. Last, peer tutors are unlikely to have the assessment or instruction skills that you will find in a tutoring center or professional tutor. If your student needs short-term help with homework, or specific skills, a peer tutor may be the most cost-effective way to assist them. On the other hand, they probably don't have the skills or understanding to be able to offer the most effective and efficient tutoring services.
Although peer tutors may have some disadvantages, there may be some distinct advantages. First, peers may know how to speak the language of the person being tutored. They can give relevant and contemporary examples for any concepts that need further explaination. This reminds me of a decidedly bad calculus teacher who responded to a students question with "I cannot imagine what it would be like to not know the answer to the question you just asked." Hopefully, you will never have to deal with such a poor teacher, but the point is, that a peer tutor might be closer to understanding what it was like not to know the basics of a particular topic. In other words, a peer tutor just learned the material themself, and they may have a very fresh way of teaching it. Peer tutors may have the leg up when it comes to motivating. When an elder presses a student to complete their work, it may sound like more of the same pressures that they get from adults; hearing such imperatives from a peer, however, may have a greater impact. Lastly, peer tutors may be better equipped to keep a student's attention.
A good adult tutor can accommodate for the advantages that a peer tutor has, and vice versa. In the end it comes down to the specific people involved, and perhaps the best approach may be to give it a try. Ask a peer tutor for a trial run, and make it very clear from the beginning that it is just a trial. If it works out, you can keep the sessions going, otherwise, you can terminate the sessions without any hard feelings.