For best, I’d suggest Schumacher/Barrichello at Ferrari from 2000-2005. Not at the top of all time, that would probably be Prost/Senna, but I’d definitely add them into the discussion. It was at the peak of Ferrari’s powers at the start of the decade, Barrichello – as much as he might not have wanted to – played the wingman to perfection, and Schumacher was all but untouchable during that period. Certainly controversial at times, but their success can’t really be ignored.
As for worst, I’d definitely agree with Sutil/Gutierrez, from the most recent number of seasons or so. Can’t really think of a more dull pairing than that. Could suggest Alesi/Mazzacane in the Prosts at the beginning of 2001, at a stretch. Mazzacane was pretty terrible (rightly, I feel, dumped four races into the season), but despite Alesi being somewhat over the hill, he still had the capability to challenge for a meaningful result, so I think that alone would be enough to keep them out of the running.