I read this as you wanting to compare max climb rates at takeoff? If you know the % of first limit in the OGE hover at a given config, then that gives you the comparison immediately. But if you want more indicative numbers....
As long as you stick in the hover/straight up there are quick (and fairly dirty) ways. I'm afraid I only know metric units.
in the hover, thrust = weight (obviously) - so calculate the hover induced downwash:
vi (downwash velocity (m/s)) = square root (mass (kg) x 9.81/(2x air density (kg/m3) x rotor disc area (m2))
Hover power (watts) is simply hover thrust (newtons) multiplied by vi - the downwash induced velocity. If you know what the aircraft actually uses in the hover at that weight, then the percent power or torque difference (actual against estimate) will remain roughly constant as long as the aircraft has zero groundspeed.
If you don't, then I think you need to add about 40% to the number calculated above to accommodate profile drag, transmission losses & the tail rotor. This accounts for the engine & transmission power that goes into things other than lifting the helo. I haven't done this calc with real numbers for about 4 years, so it'll be a bit rusty!
Anyway, once you've got an estimate of hover power, you need to establish how much more power is available (watts). Then the rough climb velocity in the hover will be: excess power (watts) / (mass (kg) * 9.81). You should reduce the excess power by whatever efficiency factor you worked out (like knock 40% off if that's what you assumed earlier).
That'll give you a rough vertical climb performance in m/s.
Don't know if I explained that well - it's based on 'foundations of helicopter flight' by Simon Newman. It'll be fine for a rough stab & basic comparisons. I used them in the opposite direction to work out torque change for a given rate of climb.
(came out within 5% of actual across the speed range, which was good enough for my application)
The excess power to climb rate bit works for all collective led climbs - for rough indications - but the induced velocity bit changes quickly with speed.
The problem is in the losses. 40% is a reasonable rule of thumb, but it can easily vary 10% each way. And bear in mind it's an efficiency compared to a perfect isolated actuator disc, not to any form of installed or practical system.
Hope that's useful?