Regarding withdrawing the underbolting, I think the snap action underlever would provide greater mechanical advantage than the top lever system.
Add to this that the hand is used with the snap action lever as opposed to the thumb with the top lever.
If the gun was "locked up", ie difficult to withdraw the bolting due to heat or whatever causing higher than normal pressures, I think the snap action under lever operated by the hand, would provide better leverage and therefore be easier to move than the top lever pushed by the thumb.
Remember that the 600NE produces very high thrust against the breech compared to other cartridges meant for use in double rifles.
This is why Jeffery has gone to what they felt is a better action design for the 600 NE to be used in high temperature countries.

Some snap action designs (as well as operating the bolting) use the underlever to cock/recock the locks.
I've never had the chance to examine a Jeffery 600NE snap action so I don't know whether the cocking is done by the lever or by the barrels.
Curl will probably know the answer to that I hope.