I went from a Canon 600D to a Canon 7D2. I recently bought a
second hand 6D.
Here's my experience.
The 7D2 is a better camera than the 6D, in every sense, except how much light you need to get the same exposure, and how it handles very low light scenes, at which point the 6D is unparalleled (and the 6D is better than the 5D2, and potentially, the 5D3 in that regard, depending on who you listen to).
You're moving from a 550D, so it might not be as obvious to you. The 7D2 has better auto-focus (faster, more points, more accurate points, more consistent success rate), it has better controls (joystick over just a thumb-wheel, and a number of additional buttons). The 7D2's screen is better. It's more responsive overall. It's a better camera.
I can't tell the shots apart, that I get with them both, unless I look at the metadata.
The FF field of view is no different to the Crop field of view if you just do the lens maths in your head. I have a 17-50mm Sigma on the 7D2, and the field of view at 17mm, is about what I get on the 6D when using the 24-105 at the wide end (I get about 26mm on the 7D2).
However, the 6D consistently needs less overall light to expose properly at a given ISO than the 7D2, and in low light, the 6D is genuinely usable up to 12800 ISO (I'd not comfortably use anything beyond 3200 on the 7D2).
I can't tell the shots apart, that I get with them both, unless I look at the metadata. (Yep, I put that here again).
My 7D2 is heavier than the 6D, but in your case, you'll notice the 6D is heavier than your 550D I suspect.
You can get lovely background blur with a crop sensor, you just need to understand how much DoF you get from your lens at different apertures, with different distances, and then exploit them. With a full frame sensor you still have to work to get blur, you just need less distance to achieve it. It's not a panacea.
When I'm using the 6D, I get frustrated by the slow(er than the 7D2) AF, by the very small number of focus points covering quite a small part of the image.