Their lyrical differences are reflected in the melodies, of course, but I would not describe Lennon's chord choices as "sarcastic", for example.
That's an overly simplistic - and I'd say wrong - characterization.
On the early albums leading up to Rubber Soul, Lennon handles a larger share of lead vocal duties. He sings ballads ("I'll be back", "Anna"), rockers ("A hard day's night", "Twist and shout") and mid-tempo songs that fall somewhere between rockers and ballads (like "you can't do that").
When he does start sharing vocal duties with Paul on Rubber Soul, there's not a single "whiny" Lennon song. There's "Norwegian Wood" and "In my life" (not to mention fillers like "Run for your life") which are written, sung and arranged in anything but a "whiny" style.
I see different accounts. Many imply his brother "cracked" the case by fingering him as a suspect, not some FBI statistical wizardry. Perhaps stylometry added to the evidence, though.
As far as The Beatles, a large part of their success is the juxtaposition of contrasting styles, in my opinion. Lennon had a sarcastic style and McCartney a more optimistic sound. Too much Lennon is whiny, and too much McCartney is syrupy and cheesy. Mix and/or juxtapose them and you get a great balance and contrast: flavor AND spices.