To burn, or not to burn.

Another option is to burn their shields off with your grenades, then bring the pain

I always take a selection of weapons irrespective of Burn modifier, arc for fallen captains, void for Vex minotaurs, etc. to get down shields before using the burn weapon. "It seems that Bungie applies the 300% modifier FIRST and then the elemental shield reduces that number by 200% due to the non-corresponding elemental damage. This would make the modifier 150% for the burn element to the non-corresponding shield element. In conclusion, it would be smart to assess the weekly nightfall to see what shield types there are, then select weapons accordingly to take down enemies the fastest. For example, if most of the enemies have void shield, yet the burn element is arc, take a void weapon to take down the shields then use the burn element to finish them off. This is smartest in a scenario where you're taking down an ultra or heavy mob." Source: http://www.reddit.com/r/DestinyTheGame/comments/2hypnc/elemental_damage_nightfall_burn_damage/

In my experience, if you have a primary with the correct burn, it will punch through the 'wrong' shield type quickly enough because it's hitting so much harder anyway. That said, in every nightfall there seems to be a few key moments were you'll be rushed by enemies with a different shield type and having a special or heavy with the right element can be key to whether you breeze through in 20mins or wipe.

You're best off bringing the shield down with the relevant elemental weapon. Then you can quickly switch to void after that, but it's a question of whether you can do that quick enough to stop them getting their sheild back. Another plan is to have one fireteam member bring down the shield and the others use void to bring the pain once they're down.