Actually...
The film you metered at EI 400 will be properly exposed.
The film you metered at EI 1600 will be two stops under-exposed.
It doesn't matter much what development you use - you won't be able to offset the two stops of under-exposure in the shadows for the EI 1600 film.
However:
If you develop at 400, the EI 400 film will be both properly exposed and will have correct contrast. At the same time, the EI 1600 film will be under-exposed by two stops, the shadows will have little or no detail and poor contrast, the mid-tones will have poor detail and muddy contrast and the highlights will have mid-tone like detail and contrast.
If you develop at 800, the EI 400 film will be properly exposed and will have extra contrast. At the same time, the EI 1600 film will be under-exposed by two stops, the shadows will have little or no detail and a bit better contrast, the mid-tones will have poor but slightly better detail and middle to good contrast and the highlights will have mid-tone like detail and higher contrast than the 400 developed contrast, which may or may not be good.
If you develop at 1600, the EI 400 film will be properly exposed and will have considerably more contrast - potentially too much contrast. At the same time, the EI 1600 film will be under-exposed by two stops, the shadows will have little or no detail but better contrast, the mid-tones will have poor and slightly better detail, but good contrast and the highlights will have mid-tone like detail and higher contrast than the 800 developed contrast, which may very well not be good.