OK, looking at these polls 538 conducted with Morning Consult, I compiled some graphs. Some basic information: Morning consult asked voters in an online survey about the candidate they support and how they rate each candidate as favorable/unfavorable. They came back to the same persons after the first debate and after the second debate. Not all answered in the followups and not all saw the debates.
For support I ignored the results after the first night, as this was only temporary. So here the support before the debates and after:
Clearly Biden was the big loser and Kamala the big winner. Warren and Sanders also look not too bad. Pete and beto lost support.
As Morning Consult asked for favorability, we can calculate a rough name recognition. The idea is, that if you have no strong opinion either way about a candidate, you probably don't know enough. So I added the ratio of people seen the candidate as favorable and unforable each for before and after the debate.
The result is pretty obvious. The candidates that were already well known, had not much growth here, while the fairly unknown ones got big boosts. That's why Steve Bullock, Mike Gravel, Seth Moulton, Joe Sestak and Wayne Messam are also losers of the debates, as they don't have this name recognition boost.
Finally the net favorability. This is favorable minus unfavorable. or how much more people liked you than disliked you.
This is kinda interesting. Unsurprisingly Joe Biden and Beto O'Rourke lost here, as they lost support. But Buttigieg favorability increased, although he lost support. So Pete-fans just liked someone else more. On the winning side Kamala did win a lot, but also Warren, Booker and especially Castro have big favorability boosts. Among the smaller candidates Tulsi gabbard nearly doubled her net favorability.