"I would expect nothing less from you" seems more formal to me. I imagine a superior military officer saying it (as praise) to a subordinate officer (who is probably standing at attention). It's not only a statement of fact but a comment on "your" character.
"I wouldn't expect anything more from you" implies that you've done the work to my satisfaction. There isn't necessarily an implication that a better person than "you" would have done more. You could make it an insult by stressing the "from you": "I wouldn't expect anything more... <pause> from *you*" or "Well, from you... I wouldn't expect anything more". To avoid that interpretation, I'd drop the "from you", like this:
"I washed the insides of the windows, but it was too hard to get to the outsides."
"That's OK, I wouldn't [or "didn't"] expect anything more." [possibly adding "... than that."]
"I would expect no more from you" also implies a judgment of character. The implication is: "You did something stupid or bad. But anyone who knows you would have predicted that you'd fail that way." It's still pretty formal. In most cases, I'd be more explicit and direct: "Of course you didn't wash the outsides. Once again, you give up before doing the hard part."