I have to add an additional comment for when comparing the BR and DMR to determined which gun is best. Most of the players do usually take a multiplayer perspective and I cannot blame them for viewing this question in this specific angle.
However, if you view it more towards which gun is most effective in Campaign, it's extremely difficult to decide as there are no missions with both the DMR and the BR. This results in that we most compare the weapons slightly differently when it comes to determined how effective they are. If any of you has played Halo 4 on LASO (Legendary All Skulls On), the main difference with the DMR and BR is actually that the DMR is powerful enough to make the Jackal fling its shield from a shot in the hand unlike with the BR. However, in any other combat situations in LASO, there 2 weapons are set to be fairly even but it do still crown the DMR to be a winner in the Campaign because of the increased effectiveness against shielded Jackals.