The sample shots are very nice, but not the sort one is typically able to attain with either a big sensor camera or a ultra-zoom P&S.
Birds have a propensity to keep at considerable distance from people, with or without cameras, except for urban sparrows or starlings accustomed to hand-outs. They also have a propensity to perch high in trees, which invariably entails back-lighting and a silhouette appearance, unless you are very fortunate. Small ones that fear raptors will avoid open spaces at mid-day. So many are apt to appear only at dawn or dusk, or hide amidst branches and folliage. You can go and sit in a bird blind all morning, and gain nothing but mosquito bites, until you decide to leave when the chattering strollers, heckling teens, and shreiking kids arrive.
No sensor, of any size, will insure you against those problems.
But it does strike me that very few of the sample shots one sees for the P&S ultra-zooms involve wild birds in natural settings. Most are of water fowl in parks or raptors in enclosures. One gentleman has unique nest-level access to an eagle lair. But folks on the ground would have a hard time (lookup up against the sun) seeing what he sees.
Finally, the big problem with any 600mm or 800mm lens is that it is very hard to "hunt" for birds or any object with that focal length, unless you know where the object is and have the time to set up your shot. Perhaps, if there is a nest or bird feeder. Otherwise, the bird will be gone before you can set up the tripod, zero in, and make sure the focus is right. Focus is darned hard to adjust manually in bright light, if you can't see the LCD or the object in your EVF is low contrast.
If you somehow manage to pass all these hurdles, then indeed a large sensor camera will give you better prospects of a clear shot. Yes, for perhaps an extra $1,000, you double or triple the prospects of a good shot, once you've avoided all the other slings and arrows.
It's all a question of how much TIME you care to dedicate. Your discretionary money for purchase of cameras is also a function of how much time your regular income leaves you free from labors needed for survival.
Don't spend the extra $1,000 it may take to built a full "kit" of m4/3 equipment, unless you really intend to forage a lot for bird shots and can accept the fact that lots of time you won't get great pictures.