I think Sondheim has explained the thematic connection quite clearly, with one being the quasi counterpart of the other. ANGEL is indeed based on just one single idea: the guests somehow just couldn't leave the room, in which they had a party. DISCREET CHARM on the contrary is IMO a better film, with a more complex structure and some better intergrated surrealistic elements. The cast of six (or seven in you count the bishop) are trying to have dinner, but it keeps getting interrupted by some incidents. That said, ANGEL never leaves you bored, because it has a bigger ensemble, and each character has his/her own thing to say, so that new perspectives are being thrown in. Both films are satires about rich people, and talk about the anxieties and insecurities of this certain class.
There is no direct connection on the level of character between the two, but since the characters could be seen as typos of people in this class, similarities can be found.