A Boyer and a Pamco are two entirely different ignitions. The Pamco was developed specifically for the XS650. By a member on here, Pamcopete. The Boyer is a system built for another bike and adapted to the xs650.
You asked "Do they do the same job as the stock ignition?" The answer is yes, Any ignition does the same job, they make the plugs spark at the right time.
The stock TCI is a good ignition. It works very well. The problem with it is fixing it when it has problems. As mentioned the only way to test the box is by substitution.
The Pamco comes as a basic unit that was designed to replace the points on the 70-79 bikes. It also replaces the TCI but needs the advance rod, advancer and bushings as used by the points. They need to be installed to make the Pamco work.
Mike's has kits that start with just the basic Pamco and build from there. You can get a kits that are complete with all you need, but use different coils. One coil uses weak terminals for attaching the wires. I don't recall which one. A search one this will find the info.
Pamcopete further improved his ignition by adding the E-advancer. This device eliminates the stock mechanical advancer. This removes several issues with the stock advancer.
Again Mike's has kits from the e-advancer up to ones that include everything.
It sounds like you have stripped the bike down and are rebuilding it. To test the ignition you will need to install the alternator rotor and stator. These have components of the stock TCI mounted on them. The rotor has a magnet in it. The stator has the pickups on it.
You will need to wire up the coil and pickups to the TCI box. You will need a battery to supply power to the TCI box and coil.
Wiring in an on/off switch is a good idea.
In the "Some Electrical Diagrams" thread found in the XS659TECH section you will find plenty of diagrams to help.
I like #4, it shows the basic points system with the early reg and rec. In boxes it has the later TCI and combo reg/rec.
Swap the early boxes for your boxes.
Once you get the parts wired up following one of the diagrams, you should get spark.
Leo