I'm of the opinion that if the congregation is going to participate in the Psalmody (which it usually does), there are only two ways to do it: complete unison or alternating by whole verse between the minister and the congregation. Don't do it by half verse because that screws up the cadence (even if you're not chanting) and don't try to be cute or creative by alternating between men and women, pulpit side and lectern side, and so forth, because it puts you all in the unenviable position of playing Fizzbin.
By the way, here are a couple of instances in which the congregation would not participate in the Psalmody:
- the kantor or a schola chants the entire Psalmody
- the Introit functions as the Psalmody