Is it the battery or the alternator?

The best way to check this is to go to a parts store and have them do a test, however the other way is to remove the negative cable from the battery while the car is running and it will die if the alternator is bad, or start to die. If the alternator is okay then it will keep running smooth (shouldn't change AT ALL when removed) because it is still outputting enough power to keep the car running or to charge the battery.

Good Luck

Without doing the run thing mentioned above. Was the wiring the same? That is the big issue. You need to be careful when cross matching parts. The schematic for the alternator is what I would look at and see if they are the same. I could track that down but the simplest by far is to get the correct alt for the wiring of the car.

do not remove the battery cable, with car running ,this will sent voltage spike to diodes when you disconnect the cable and when you reconnect the cable,you could weaken the diodes,put voltage meter across the battery terminals ,with car running should read 13 to14 volts, not running 12 volts,while car is running if voltage read 12 volts replace altenator

What I've seen so far-a lot of aftermarket stuffs on it.

Disconnecting a battery cable is a bad practice-uncontrollable voltages will kill the rectifier as mentioned.

Engine not running measure the open voltage of the battery should read atleast 12.4 or better.

Now fire it up measure it again should read somewhere between 13.5 -14.5 if not the alty went south bound-I know what you're thinking, forget about the voltage regulator-change the alty. its okay if the VR is an external.

HTH Good Luck