Once your above lasing threshold, the diode output generally follows the current till you get close to the knee of the current curve, then increasing current decreases output power and then comes failure mode where the diode still conducts but you blow the mirror surface off the lasing face. In principal, you would just have to back off on the drive current to the newer, brighter, diode.
Generally if you have a constant current source with a trim pot for setting current, exchanging diodes is fairly easy.
Provided you start at a very low current setting and can monitor the current by some means.
We generally use a "Dummy Diode" test rig consisting of a two ohm 2 watt precision resistor and three or more 1N4001 in series to simulate the diode drop. The number of 1N4001 used is based on the forward voltage of the new diode from its spec sheet. This lets us calibrate the constant driver without endangering the laser diode.
What would catch most people is that diode cans are generally pressed into the brass collimator mount with a force fit. So you
have to get the old diode out without destroying the collimator mount. This usually can be done, but you will destroy the old diode in the process. You will also have to refocus the collimator.
Not to mention there are 9 different pinouts in common use, of which I generally see the same three over and over.
Adding a series resistor will not help you. The diodes run off a constant current, not a constant voltage source. They have a negative delta and will thus run away to destruction without current limiting.
All bets are off if the diode driver runs in constant light mode instead of constant current mode. This happens if there is a feedback photodiode mounted inside the diode can or off a beamsplitter down stream. At that point your into some serious reverse engineering.
Roithener Lasers in Germany usually can source the older diodes, inexpensively. Its worth a Google.
Steve