I have a BBSHD as well as a Tangent with proportional PAS.
The Bafang is very smooth and virtually silent. PAS programming out of the box is poor so you need to do your own before it works well. Once you do it is great but not proportional. That's not really a big problem but it means you will be adjusting your PAS levels when load changes. It's not set and forget.
Proportional PAS with the Tangent is great. You set your assist level for your type of ride and rarely, if ever, change it. Throttle is less needed as well compared to the Bafang. You just ride the bike like a bike and it does what you want. The difference is significant.
Regarding noise, the Tangent is louder without a doubt and it's noise is a combination of some whine and some coarse grinding type noise. It is not loud and cannot be easily heard by others off the bike, at least with PAS. The Tangent comes with some vibration. I find the noise just fine, I'd like the drive to improve in the vibe department.
PAS isn't perfect on the Tangent but the shortcomings aren't with the drive but rather the Thun BB and the CA. The BB only reads left side power and only has an 8 pole cadence sensor. These shortcomings combine with the CA firmware to cause a sluggish and inconsistent turn on from a stop. It's not as responsive as you'd like. You can mitigate that somewhat with CA programming, but when you do you will get some motor run-on when you stop pedaling. On the Bafang that's pretty bad but with proportional PAS its not a problem at all. You can't, however, fully eliminate the sluggish starts. I believe Grin knows about this and Dave does too, but the problem doesn't lie in anything Dave controls. Grin has promised improvements in this area. Other than the sluggish starts, PAS is pretty glorious.
So the TL;DR is that the Bafang PAS is smooth, quiet and refined so long as your program it yourself. The Tangent is less smooth, quiet, and refined but the proportional feature is fantastic plus the Tangent is a much nicer package with vastly more power and lighter weight. Tangent requires more regular maintenance, greasing every 100 miles, which might be an issue for higher mileage commuting.