The Elkhead Pass route is DEFINITELY worth it while ascending and descending Belford/Oxford. It adds about a mile but is a much easier climb/descent, plus there are spectacular views at the pass not available atop either peak (see photos below).
The good news is that I was smart enough to ascend via Elkhead Pass (and camp out the night before, to get an earlier start) and catch spectacular sunrise views. The bad news is that after bagging both peaks I descended the standard Belford route, which was murder on both my quads and my feet (I'll be losing 3 toenails in the upcoming weeks). If I could go back in time and change anything, it would be to both ascend and descend via Elkhead Pass.
Also, there is no water available on the standard Belford route but water is available on the Elkhead Pass trail until just below the junction with Missouri Mountain. So if you head this way you could carry less water or reduce the risk of running out. I saw a number of late-starters ascending Belford up that murderous slog in the heat of the day run out of water.