Yes, it sound like a strange question but it does matter lots of times. If not, I probably wouldn't be writing this article.
Let's get started. The question here, as the title says, is to discover if we want to take a round-trip with one single airline or we prefer to go with one and come back with another. Again, the answer is not obvious but there are many things that can be said to give you a bit of guidance.
One can think that if you can find a good price with an airline to go but the price to come back is pretty high, the competence will have a lower fare. Well, could be, but rarely. If on the day that you come back the fares with your outbound airline are high, it probably means that competence will also have high fares on this day. The market is the same, and as the reason for a high fare is the high demand, it would be strange that two airlines covering the same route on a same day have different demands, wouldn't it?
Now that you agreed, I'm going to say that this is not always like this, and the exception comes when we are talking about horrible timing flights. I call them like this because they really are. You need to wake up at 3:00 am to get to the airport at 5:00 am because your flight departs at 7:00 am. Good, you have probably found a good airfare here, in case that the competence does not flight at the same time, of course!
There is a general rule that also applies. Whichever route you choose, the hot deals will nearly always be for round trips, not for single flights. This puts you on trouble if you manage to find a good offer with another airline. If you fly with one and come back with the other, you can't get the bargain but at same time the price to come back with this other airline was extremely low! It is not easy, but if an airline has a good list of discounted round trip deals, almost sure the best option you can take is those deals.
At same time, flying with one single airline will allow you to accumulate miles if you join one of their frequent flying programs. If you go with one and come back with the other, you will always end up having points with all airlines but none of them will be redeemable for anything as the quantity will not be high enough. In any case, actual alliances make you able to change some points from here to there, so you should contemplate this option too.
After all, I would say that normally you will find the best deal flying with the same airline from all points of view, and I only recommend you to fly with another in case that the circumstances of the trip offer clear advantages to you. In this case, keep in mind that you are sacrificing miles for a slightly better price, so think deep about it before taking the decision.