Truth is, both can be done well. Both can be done poorly, although I think it is much easier to royally destroy a Mass facing the people than it is to do so to a Mass celebrated facing the apse/in the same direction as the people.
Tradition is a good argument for having Mass facing the same direction as the people. It cannot be denied that for the vast majority of the Church’s history, Mass was almost universally celebrated with a common orientation. This is simply fact, and this fact at least requires our consideration as to why it was done for so long. After all, it obviously had (and has) value.
Mass in a common orientation has other good arguments in its favor. First among them is that it is symbolic of the priest and people facing in a common orientation, that is, “going toward” a common end, which is Christ. The True Faith being linear in its eschatology, this is very fitting. Also, Mass in a common orientation virtually guarantees that the priest will not give into human inclinations and feel as if he is doing the Mass “at” or “toward” the people. These are only a few of the arguments in favor of this liturgical orientation, all of which are quite practical and reasonable. Some people will say, all these weren’t the reasons why Mass in a common orientation historically developed. I say, so what? That’s fine. These only add to whatever reasons were used to originally justify this orientation.
Mass facing the people has, as far as I can tell, only one truly good argument in its favor, which is that it (sometimes) allows the people to see the consecrated elements on the altar from the Consecration forward. This is certainly a good thing. But I say sometimes because, very often, the hosts are not visible since they are contained in a ciborium, and the Precious Blood is always in a chalice. These things are always opaque, or they should be.