I guess in general, it is better to use weapons with the current burn damage. Even though it is not the right type for some shields, burn damage will wear down any type of shield really quick.
In the end, it's a matter of cost/benefit, if you have good weapons of all sorts, it should be appropriate to combine types of elemental damage.
But, from my experience, it is worth filling all slots with maxed weapons with the burn damage for nightfalls, because you can cause a lot of damage to non-related shields and when you have them down, you'll cause massive base damage to enemies.
Yeah this is what I've normally done but I've seen people running nightfalls with all their weapons equipped with the burn damage of the week, was wondering if I had been wrong this whole time haha!