Aight people this is simple, recount only records your DPS as long as you're attacking the boss, "Example"
Player A pops all CDs hits the boss goes to 15k DPS, stands back and goes afk for the rest of the fight, DPS drops slightly from DoT ticks.
Result: 14k DPS, 250k Damage done
Player B pops all CDs hits the boss goes to 15k DPS, keeps attacking after CDs wear off, DPS drops to 13.9k by the time of the kill
Result: 13.9k DPS, 2.5 Million Damage done
The way recount works makes the "DPS" listed inaccurate, it does not show your DPS from Pull until Kill of the boss, but DPS while actually Attacking, which makes it useless to settle your bet.
If you want an accurate result, take damage done (For each of you individually) divide it by the ammount of seconds the encounter took, and you have actual DPS for the encounter.
Put to use on the examples above:
Say the encounter took 2 minutes, "120 Seconds"
Player A 250k damage done, divided by 120 seconds
250.000/120=2083,33 DPS
Player B 2.5 Million damage done, divided by 120 seconds
2.500.000/120=20833,33 DPS
Hope this answers your questions