Taking the compressor side first. It depends what problem you need to solve. Two compressors in series give increased pressure. Two compressors in parallel give you greater volume. But this applies to free air effects, ie, without an intake manifold. plumbing or intercooler. If your intake path has significant impedance, the parallel setup won't come close to doubling flow, but the series blowers just might.

With a series configuration, the turbo impellers might benefit from being asymmetric, because the second turbo will operate under greater load. This is because the first compressor creates higher pressures (and thus greater density) at the impeller of the second. So the second compressor consumes more power to further compress an equivalent volume of gas. Asymmetric compressors should also help turbo lag: the lower powered compressor would likely spool faster. You could probably get further benefit from an intercooler between the stages.

With parallel operation, I think the turbos have to be symmetric, otherwise the slower compressor will bleed flow from the faster compressor.

On the impeller side, there's no advantage, and considerable disadvantage, to series operation. The first impeller would simply reduce the energy available to the second. So regardless of how the compressor side is arranged, the impeller side will always be parallel.