The last vacuum to go over the carpet will always pick up additional dirt than the previous vacuum because the agitation from the first vacuum raises the nap and combs the fibers up. Then when you go over it with the other vacuum, it has a clear air path down to the backing where it finds more dirt. Kirby salesmen love to exploit this when they demo vacuums in homes where they have you use your own vacuum first, and then they go over it with the Kirby and it "magically" picks up more dirt and then presto they get a sale. You could go over it with a Dirt Devil even and it would still pull more dirt out (not hating on Kirby - just stating what the sales tactic is).
The Rainbow E2 black is a water filled straight suction tank vacuum with a power nozzle, the Kirby is a full size HEPA upright. You cannot compare them as to who is better - it is apples to oranges. Contrary to belief, I do not think this is is a battle of Kirby owners vs. "the more money you waste the better it is" owners.
What I think might be happening is it is just simply an issue with the carpeting and how it is made today. Carpeting has recently started being made with rubber backing for better flexibility and spill and germ resistance compared to your standard nylon weave backing.
If your carpet backing is rubber this further exacerbates the problem because vacuums will grab right to the rubber and form a seal when they get close enough to it. Kirbys have a lot of suction, and if you give them the opportunity, a Kirby will eat a throw rug whole.
The Rainbow's nozzle is a lot lighter than the Kirby and looks to be plastic, so it floats across the top and doesn't really weigh down the carpet much. The Kirby is heavy, and sinks itself into the carpet (you mentioned you had berber, it looks like a plush nap in the photos). When this happens, it creates a similar effect to the blowing into a bottle metaphor. The vacuum has suction, agitation, etc, but there is no airflow passing though the ultra thick carpeting around the nozzle for the vaccum's suction to lift it out and remove it. So the vacuum is sucking on the carpet with all its might, but nothing is being picked up and carried through into the bag. You can't raise it up any higher obviously as then you won't get deep into the carpet to agitate it. This explains why you are getting all the fine debris off the surface, but the heavier stuff is getting left behind that is deep in the carpet pile.
Usually vacuums become harder to push when they start gripping into the carpet too much, but because the Kirby has power drive strong enough to push furniture out of the way to help motor it along, it usually will go unnoticed.
When I was Googling this problem - I actually found a Vacuumland topic from 2013 of the same circumstances you described - Kirbys hard to push on berber carpet.
https://www.vacuumland.org/cgi-bin/TD/TD-VIEWTHREAD.cgi?23005
If you skip down to Post# 257931 on that link, there is a mention of changing the brushroll to a softer bristled brushroll for delicate carpets on the Sentria. Maybe that is what you need too?
This all just my theory and I make no claims of it being correct, it's just my best guess on what's going on since you went over the entire Kirby and everything is all in order, and the Rainbow is also working properly, so there's not much left that could be the issue other than the carpeting. Good luck!
PS: Here's a Consumer Reports report on vacuums and ultraplush carpeting.
