Ive watched a lot of Championship football over the last few years, so while I havent watched Swansea specifically Ive seen a fair few of their games.
My opinion is that under Martinez they were very good, played good stuff and got their share of results - but lacked a little something.
I dont recall much of them under Sousa, except that they seemed to be very very similar to under Martinez.
Under Rodgers all that Martinez did well got dialled up to 11. Martinez had certainly done a lot of groundwork, which I am sure Rodgers is most grateful for, but Swansea became much "more" under Rodgers. More composed, more resilient, more confident and the system of play they now have was really developed.
Would I give him the job? I would be very tempted in all honesty. While a record to back him up would be preferable, I do genuinely think you appoint the MAN and not the CV. For me Rodgers looks like he has everything we need, he has a very dignified manner which the fans would like, he has a philosophy of attacking possession based football which the fans would love, he has players who were in league 1 a few years back looking totally at ease in the premiership. He has experience of top clubs, and is a disciple of the Barca way. And he would have plenty to work with at the club. While I think Redknapps time is done, its only right to acknowledge he has done a great deal of work with the team (probably not unlike Martinez at Swansea)