You will never( hardly ever anyway) see Lesser on a peanut feeder either.
Lesser has declined drastically in recent years, while Greater has increased by 300% + Coupled with that, Greater will actively predate chicks of Lesser by digging them out of the nest.
Damn! The smaller size of the juvenile and the red cap fooled me. So I'm still yet to ever see a Lesser and very rarely get a fleeting glimpse of a Great.
It's the Greens that are by far the most common around by me.
Lesser can be very hard to see, even more so since the population has crashed. Best time is spring before leaves are on the trees. They are tiny sparrow-sized birds and stay high in the tree canopy almost the whole time. Not bold and easy to see like Greater. Listen for weak drumming- softer than Greater's and dies away at the end, not stopping abruptly. Also call 'kee kee kee'(like Kestrel) not shared with Greater.
I'm yet to see a Lesser, and only ever seen a Green once (I don't believe the is much appropriate habitat near me), but then I don't see Great very often (I got some great views of some the other week, shame I didn't have my camera though ).