Assuming we are using rank 5 take aim and rank 5 steel shot as a base and mercer's will not be critting:
R1A = 96.25 for steel
A = 85 both guns
C, P = 0 since no critical hits nor powerful ability ranks for either gun
Mercer's Pistol: Rank 8 Take Aim and Rank 5 Steel Shot gives S1=2.5 and S2=2
Beckett's Pistol: Rank 5 Take Aim and Rank 8 Steel Shot gives S1=2 and S2=2.5
Minimum damage when using a full take aim meter (hence the times 3):
Mercer's Damage: D=1.5*(26.5+96 + 0.5*0)*2.5*2*(1 + .005 * 85)*3 = 3927.65
Beckett's Damage: D=1.5*(26.5+96 + 0.5*0)*2*2.5*(1 + .005 * 85)*3 = 3927.65
Perhaps
@Beggar can confirm this since he has both weapons, but clearly one can see that they do the same damage in this case; but the specific question is if they don't use full take aim. The full story with the take aim ability is that it is a multiplier from 1 to 3 depending on how long you hold the aim, maxing out at 3 when full. The increase of the multiplier as the aiming technique is used is approximately linear, meaning that you will get the same proportion of multiplier increase relative to how filled the meter is. So, a half filled meter half the bonus damage which would be a multiplier of 2.
At the end of the day it doesn't matter how full the take aim ability because both guns (when using steel shot) will deal the exact same damage when both aimed the same amount because they will both deal the same base damage * whatever the particular take aim multiplier is in the test. So no, Mercer's does not need to be aimed longer in order to do the same damage as Beckett's in this scenario.