Prunus cerasifera 'Nigra' is a medium-sized, round-headed deciduous tree. This tree does not usually need pruning and be spoilt by pruning and.
I have this tree in my garden and a lot are grown in gardens in my village. It is easy to spot the over pruned ones as they then grow badly out of shape, with most of the new growth perched at the top.

However, if you want to prune it is best only lightly pruned in late winter or early spring. unless the tree has 'Silver leaf' in which case prune in mid summer.
THE RHS recommend if you do prune it to do it as per 'Pruning group1.

Hello there ... I believe the tree, prunus cersifera (nigra type) is at its base a plum, or grown on a plum graft. I would not cut this back during the autumn/winter period, but immediately after the flower/berry has cropped in the summer and the sap is still rising. All stoned fruits such as cherry, plum, damson etc are highly susceptible to disease (silver leaf being one) if pruned when the sap is going down. Apples and pears are pruned in the late winter to early spring, other stoned fruits in mid to late summer depending on where you are in relation to leaf drop or fruit. Hope this helps.

Sorry ... PS: Both your suggestions are based on the plum base. No disadvantages that I have heard of. The pissardii i believe makes a good hedge, so can be trimmed back during the summer to whatever shape you want it to be. As a free standing more 'open' tree, with loads of blossom, I would personally choose the Prunus cerasifera 'Nigra'.