I've tried both and I would say it depends on your situation (financial, free time , how much you enjoy teaching, how much you can pick and choose your partners, how well you are able to organize your own exchange). So, here are some differences:

1) You have to pay the teacher, you don't pay a language partner. So if you are short with money a partner can be better.

2) On the other hand, you have to help your language partner with your native language. Therefore if you are short with time or just don't like teaching, a teacher could be better.

3) With a language partner the whole burden of your own learning is on you. You have to prepare in advance something to talk about if you want it to work well. I hear that with (most) community tutors you should preferably do the same, but it's less bad if you don't, because they tend to have some sort of a backup plan, or at least some more experience coming up with topics. I've been repeating the same topics with tutors as well though.

4) Tutors are quick and easy to find, to pick, to change, and they are reliable. You know they'll show up. Finding a good language partner may be hard and take time.

5) With partners it is more personal, which can be a good thing or a bad thing, depending on how well you get along, how much you enjoy / are nervous about meeting strangers online, and your priorities in terms of meeting people vs. just learning. Even though, the fact that you are having one on one sessions can make it more personal with tutors too, compared to a classroom setting, especially it they are community tutors and not professional.

6) You have responsibility to your language partner and it doesn't feel good if you have to tell them it no longer works for you. You have no such responsibility to a teacher.

It depends. Maybe you should start by asking some different questions like:

1.'what are my goals for my target language and can only using Language partners help me do that?'

2. 'How quickly do I want to achieve this goal?'

3. 'How much time do I have or am I prepared to look for the right language exchange situation?'

I agree with most of Katarina's points.
I've tried a couple of language exchanges and they just didn't work out. Some because of what Denis mentioned, guys who were looking for more than learning a language, which really s*cks. The others just didn't really work, because you do end up just kind of chatting without correcting each other. I didn't feel I was advancing at all.
I absolutely love using teachers, especially for Spanish, because you can get an hour lesson for like $5. You can tell the teacher exactly what you want to do and yes, he will show up! It's effective and you don't have to worry about alternative intentions.

Maybe it's me or my native language demands but do you know how many actually committed people I've met? 0! I've heard that finding a study partner is easier for ladies but the true intentions of those guys are far from learning. Don't know if it's true, don't quote me on that. 

Also, I believe that common ground is vital for the interaction. Otherwise, the communication becomes tedious very fast. The tutor, on the other hand, does their job, and everything in the process is about you and your progress. A financial reward is all that is needed from you. Sorry if is sounds too direct and cynical.

Still, I've got high hopes that I'll meet someone dedicated to studying with.