Neither would be my first choice but if it came down to it, Potter all day long, the Chelsea situation was unique and I don't think should be used to define him as a manager, ignoring this I do not think he has demonstrated previously that he has what it takes to manage a top level club, however I do not think he would be a disaster, I think he would probably make us more consistent and improve on the basics (not hard given the current state)...
That said do not really want Southgate, he has not demonstrated any capacity to manage at club level let alone a big club (previous club management was poor), it is much easier to transition from club to country than vice versa IMO, but I am not knocking what he has done for England, I fondly remember Robson and Venables, but he is the best manager we have had and he really has done great (could probably have done even better), but I dread him as our manager
Either way would give both a fair crack of the whip if they were appointed, I was pro ETH before he came and have only recently become disillusioned with him, I try not to be a negative Nancy too early in proceedings