Both the Provari and Lavatube use a one battery configuration and a booster circuit so your going to be amp limited with both due to the one battery configuration, you can't get blood from a turnip. If you want a VV that handles dual core across the entire range you need to look at mods that use a dual battery configuration and a regulator with higher current specs.
The Provari and Lavatube have the same current cutoff and use and use a high drain 18650, results should be similar with a dual core or any carto/atty for that matter. The current limiter works a little different in each though. Once you go past the limit in the Provari it gives you an error code and won't fire until you set it withing spec again. The lava tube won't stop working it simply scales the regulator down to a safe current level when you try to operate it at a higher level.
In short if you go to high on the Provari it won't work, the Lavatube will work but it won't be at the voltage showing on the meter, the regulator will be scaled back.