The company I work for primarily uses Bosch as the video surveillance and recording solution for the correction industry. We are also an Avigilon partner.
My opinion is the Bosch Video Management System (BVMS) is a far better enterprise solution over Avigilon. The Video Recording Manager (VRM) acts as a video data traffic cop. VRM records video data across all the iSCSI storage as if they are were a single pot, so to say. You can also create separate pools if you need to. Avigilon, like a majority of other vendors require you to allocate your cameras to specific storage arrays. VRM will also allocate span blocks to other storage arrays automatically if a storage array goes offline for whatever reason.
Avigilon is much faster when it comes to searching for incidents. Especially when you utilize the appropriate filters. Bosch isn't bad though.
I'm just getting used to the ACC software of Avigilon. It's pretty easy to set up and use, but so is BVMS. In my opinion, BVMS is the better option for viewing live video. I dislike the numerous "sites" you have to set up with Avigilon (and most other vendors) because the IP devices are allocated to specific servers. With BVMS, all your devices are under one easy device tree and you set up what the user "sees" very easily. You can get the same result with Avigilon, just with more hoops to jump through.
Both Bosch and Avigilon have excellent analytics. In both cases you have to use the vendors software to get the most out of the IVA in the camera. I've found that Avigilon's ACC software is very installer user friendly in regards to IVA. Bosch takes a little more time as their documentation absolutely sucks. All in all, they are very comparable.
Both Bosch and Avigilon support 3rd party cameras as long as they are ONVIF Profile S compliant. I've had no problems bringing Axis cameras into BVMS. I haven't had an opportunity to connect 3rd party cameras to Avigilon, so I cannot give an opinion on them except for what the data sheet says. You will most likely lose some functionality a 3rd party camera may have when you use BVMS or ACC.
As of today, Avigilon's licensing beats the pants off of Bosch. With Avigilon, you only buy camera licenses at the initial sale. You only need to license the sever (each server) when a new software version comes out. Also, Avigilon clients are unlimited. With Bosch, you have to basically license everything. You only get a small number of free channels and simultaneous client licenses with BVMS Pro (enterprise). You have to purchase a Service Maintenance Agreement (SMA) for each individual license if you want to upgrade. The Bosch DIP2000/3000/5000/7000 units come pre-licensed from 16-32 channels and 5 workstations. These units have a maximum of 128 channels and 10 workstations. No SMA required as you can upgrade the units to the latest at anytime (hardware permitting, of course).
I'm still a newbie in regards to Avigilon, but at this time I only consider them for smaller projects (1-48 cameras) until I'm more familiar with them product. I love the Bosch product. I've had my frustrations with BVMS over the years, but overall it is an excellent VMS solution.