I've been running a bolt release and lefty carrier for a long time now, and they both do two different jobs (well each does one really well).
Bolt release - It's secondary use is to lock your action open for IA's & Stoppages, but more importantly to "release the bolt".. when reloading the bolt release gives you the ability to quickly drop the carrier on a new round in the shortest time possible.
Lefty Carrier - Used to clear action in IA's & Stoppages, Most importantly to "#### and shoot" with our non firing hand (unless you're a lefty savage), it also allows you to maintain your rifle in a heads up position.
BOTH - When used together allow the shooter to do everything from feeding the pig, reloading, address IA's & stoppages all while maintaining an alert position, no unnecessary hand movements and increased overall speed.
Is one more important/more useful thant he other?? IMO from running both, the bolt release is MY most important upgrade. It allows me to reload fast. IA's, Stoppages & loading can be drilled using the eastern doctrine to great effect. There are only two ways to reload the rifle.. tilt & recock or hit your bolt release. Bolt release is the fastest. But IMO they compliment each other and when used in conjunction really help get you in the game with the least amount of movement/brain power.
Most importantly for us western oafs, having things like buttons for our little piggies to touch provides a better muscle memory. We like our rifles like remote controls in the West. More buttons, more speed, more power, less energy.