I have a LCR 357 with the LaserMax and my wife has a LCR 22 with the Crimson Trace. We've shot both LCRs with each laser and we prefer the LaserMax. In fact, my wife wants to trade her LCR 22 with Crimson Trace for a LCR 22Mag with a LaserMax. For us, the Crimson Trace inevitably flashes on when least expected, like when drawing the gun from a holster, and, unless we take care to adjust our grip to activate the switch, it doesn't turn on at all, like during rapid fire drill.
The LaserMax is more direct: Turn it on only when needed. Some people claim that in the heat of the moment the shooter may forget of activate the laser. Perhaps, but the shooter may also forget to turn on his/her flashlight when needed and may even forget to pull the trigger.
The only downside to the LaserMax is there are no holsters for it, yet. Some generic Nylon holsters have sufficient clearance but the laser activation switch can snag on the stitching.