Heya,
Depends on what you shoot.
If it's birds in flight, action, lots of tracking and panning, go with the 400 F5.6 prime. Or even hunt down a 300 F4 or a 400 F4 depending on budget.
If it's just stationary wildlife, maybe some flight on larger birds, and you need to maximum reach to get maximum pixels on target, then 600mm is the way to go.
There's lots of debate about 400mm cropped vs 600mm. The reality is, 400mm cropped has less pixels. When you're already reaching out to even begin to fill a frame, having a longer physical focal length is superior to cropping a shorter focal length. This is also very dependent on the camera and it's resolution, as cropping an 8MP file is quite different from cropping an 18~20MP file from one of these lenses.
There's not a huge advantage of 600mm over 500mm since you already have that. Going down to 400mm is something I would not consider, again, unless you really want something sharp at F5.6 and fast to autofocus so you can track things moving quickly, like a bird in flight, or things just running/moving fast. If you want to reach out further and increase sharpness, the Tamron will do this. It's fast enough for birds in flight, but it's more suited to stationary stuff. Also, the VC on the Tamron is quite effective. I can get down into the double digits at 600mm handheld. If you're shooting action and panning, you don't care about IS/VC, so don't worry about it. IS/VC depending on it's type (modes), comes into play depending on whether you're doing stationary stuff, or if you're panning specifically. It's not an always on top thing, it's a tool you use when it's useful. It's not always useful and sometimes needs to be off.
The difference between 400mm and 600mm is pretty significant.
Here's 400/500/600. This is a big great blue heron. It already was very far away (600mm on APS-C and it only fills 20% of the frame? Far away!). This is where longer reach is very important. More pixels on target. And it's a noticeable difference side by side. Not just a little.
150mm to 600mm same target, Series
As for the VC of the Tamron, here's 600mm with VC on, hand held, at 1/40s.

IMAGE LINK: https://flic.kr/p/qbSNpN
IMG_1674
by
Mwise1023
, on Flickr
As for sharpness at 600mm, well, here's some examples:
IMAGE LINK: https://flic.kr/p/npdm8o
IMG_3484
by
Mwise1023
, on Flickr
IMAGE LINK: https://flic.kr/p/qsAoXh
IMG_2997
by
Mwise1023
, on Flickr
IMAGE LINK: https://flic.kr/p/qsAs73
IMG_2948
by
Mwise1023
, on Flickr
IMAGE LINK: https://flic.kr/p/mNPeQj
DPP_1802
by
Mwise1023
, on Flickr
IMAGE LINK: https://flic.kr/p/q1dFyx
IMG_1953
by
Mwise1023
, on Flickr
I hand hold everything.
600mm that is sharp and has VC that is about 3lbs. Great for the cost-conscious wildlife shooter. Is it the best? No. 600 F4L is pretty insane. But it costs as much as a new vehicle. Versus the above is possible with a $1k lens, which is as cheap as 600mm without a TC gets.
Very best,