Christian tends to fail because it's rarely even art. Instead, we've dressed up our convictions as art forms so that our music is little more than rhyming sermons, and our films are just scripted church services.
(Of course, the problem isn't just a Christian one. How many popular songs are examples of good art? The pop/dance numbers I hear people listen to certainly don't impress the artistic side of my brain, and neither do the popular films of the day, which happen to be slasher films or political documentaries. Maybe art is dead everywhere. I digress.)
If a Christian song accomplishes little more than a sermon or journal article, then we aren't making use of the medium of music very well. Consider Handle's 'Halleluja Chorus' that we hear every Easter; the lyrics are pretty simple, but that's not what we remember about the tune. Instead, it's the way the very music (even when it's just played on instruments) seems to symbolize victory and redemption. We revel in the excitement of that music and in the knowledge that the feeling of overcoming is one that we have every right to claim.
Today's Christian "artists" often seek to explain everything in great, verbal detail, but that leaves an empty canvas.
Explore a medieval cathedral and you'll see what I mean. The building is designed to gear our minds toward meditation and that's why so many non-religious people over the years have found themselves unable to raise their voice while visiting an old church; there's just something about the design that makes you want to think about Higher Things and be respectful. The building, itself, causes you to consider that there's something greater than yourself that deserves respect. (This is much more effective than just telling people to be quiet, and serves a better purpose, too.)
Try explaining the concept of redemption to a person. It's not easy. But I've seen a fresco painted on an old church wall that depicted Redemption without words. In the first panel Adam and Eve were in the garden as God is finishing creating the universe. Next, the garden is shown to be withering as Adam and Eve are forced out. In the third section, people are shown working in fields as Christ's birth and death are shown. Finally, Christ is shown in Heaven taking people to a new Earth that looks the way Eden did in the first section. The story of God redeeming His creation couldn't be more clear and it could be taught to a child in this way.
Of course, here I am trying to explain that painting in words and I can tell that it's not having the same effect as seeing it - there I go proving my point. It's frustrating to try and explain these lofty concepts, but maybe the Lord gave us art so that we could find other ways to express these things.