Background: I started out doing 2 gal batches and moved to a more traditional cooler mash tun doing 5 gal batches with propane burner. I then 'downsized' to a 10 liter BIAB batch inside on my propane stove and found that better suit my style and brewing habits. Last summer, I purchased a 6.5 gal Anvil Foundry to get off the propane and give myself the flexibility to brew on the same set up year round.
Personally, I really like the Anvil Foundry. I have not tried any other AIO system, so I cannot really give you a true comparison. For me, having a system which fit my brewing preferences (10L batch size) comfortably was the biggest reason for the choice of the Anvil system.
I have helped several brewers with their 10.5 gal Anvil Foundry set ups, mostly in how to modify the profiles in BeerSmith. The biggest plus in my experience is being able to set up the system well ahead of time and then having the strike water hot and waiting for me when I am ready to brew. Downside is that it takes a bit longer to clean up. Net result is no real time savings, but the stability of the mash, lack of a need to move the kettle from the stove to the oven to keep warm and then to the sink for chilling, and the ease of use are the biggest gains. I get nearly the same mash efficiency as I did with my stovetop BIAB set up: slight decrease from 86% down to around 83%. I do not sparge with the system, but use it as a full volume mash and so far it has fit anything I have wanted to brew comfortably.
I do recommend getting a bag to line the mash pipe (or even bypass the mash pipe with a false bottom). I have made great use of the optional pump to help with recirculating during the mash, setting up a whirlpool during cooling, and transferring to the fermenter. On my smaller system, the boil at 120v is reasonable and at 240v it can be pretty vigorous. I have heard people complain about the vigor of the boil on the larger unit, but it is still a boil and will make wort. I have come over to the camp of a mild, rolling boil over a vigorous boil as better for stability anyway, so it does not bother me too much to be running at 120v at times. I have dialed back the boil when running at 240v to around 80% power and probably dial it down a bit more.
Most of all my ability to move the unit from outside, to the garage, or even inside during the winter and keep the same system set up and profiles has been the biggest gain for me.