Last time I looked at data about this, it appeared that even a poor father who was present was better than no having a father in the home. If I remember right it was measuring the likeliness of a teenager to end up in prison. If there was a segment of fathers that were worse than not having a father, I don't think it shows up in any study I've seen.

Gilder's Wealth and Poverty book cites a lot of studies and examples showing how society has changed in ways making it harder for dads to stick around with everything from how drug policies are enforced to the way that welfare resources are allocated.