You need an EQDirect cable (if you want to remove the HC), or else a USB-to-serial adapter that then goes through the HC in "PC Direct" relay mode. I use the former, as I found the latter (my initial solution) to be prone to hanging.
For visual, there are pros and cons - typically, I prefer not to use my laptop and instead use my iPad and HC in combination. For AP, there is no comparison, EQMOD is the way to go (coupled with the absolute godsend that is plate solving).
So what i can gather here, is that the NEQ6 will be great because of its payload capacity and the software you can acquire to image. It will also be good, because if i buy it locally (BINTEL) i will be able to get support. it also is of great quality and tracking.
Well, when faced with the same choice, I went with the next step up, the AZ-EQ6! With a smooth (and quiet) belt drive, dual encoders, ability to go Alt-Az for visual for EQ for imaging - it's a 'do it all' mount. And not that much more than the NEQ6.
The NEQ6 will certainly give you more scope options than the HEQ5 or AVX because it has a greater payload capacity. I have a NEQ6 and am very happy with it - its quite versatile, and I have had a variety of scopes and camera lenses on it. Its more expensive than the HEQ5 as you know, but less than the AZ-EQ6 (which admittedly has a few extra features). Guiding is nice and smooth on my NEQ6, and I use a EQDIR cable that I purchased from Bintel to control the mount from my computer.