The first step is to look at the detailed battery information from the System Information/System Profiler for each battery.
Charge Remaining (mAh): 5587
Fully Charged: Yes
Full Charge Capacity (mAh): 5611
Cycle Count: 289
Battery Installed: Yes
Amperage (mA): 0
Voltage (mV): 12420
Pay attention to the Full Charge Capacity and cycles for each battery.
The second step (assuming my guess that you have a non-unibody Mac where the battery is user-replaceble - swappable without removing the bottom of the Mac) is to run a simple calibration charge cycle on the new battery (and followed by the old one perhaps to compare). Once your computer gets to know the new battery (it guesses based on average battery performance until it determines the chemistry particular to each battery that gets used over time).
The third step if you really want to measure everything on both batteries is to use the pmset -g pslog command to document each battery as it powers your Mac from full to the low power shut off point.
Here is the relevant section from the man page linked above:
If your system suddenly sleeps on battery power with 20-50% of capacity
remaining, leave this command running in a Terminal window. When you see
the problem and later power and wake the computer, you'll be able to
detect sudden discontinuities (like a jump from 30% to 0%) indicative of
an aging battery.