If the aircraft is pitching up and down a lot in LVL CHG (up to a point where the aircraft levels off momentarily), than it's better to use V/S. But if you don't want thrust to vary, the idea would be to select a higher-than-normal speed (to keep A/T in climb thrust) and just maintain approximately the desired speed with V/S.
To put in in other terms, let's say you are flying in LVL CHG with speed 280 kts selected and the airspeed is varying a lot, which causes the aircraft to pitch up and down, while having ROC between 1500 and 0 ft/min. The solution could be to just select speed 300 kts, V/S 800-1000 ft/min or so and you'd have a safe speed and a constant climb.
As far as I can remember, you can't do this in a 737 unless your airspeed is strictly stable or increasing, otherwise it reverts to LVL CHG.