Only used Tapestry. Think it's brilliant. I don't know what either software has in terms of advantages but I found it easy to use and got regular updates from nursery so just have been easy their end too!
Depends on what you want from it. Tapestry is great for observations and linking to EYFS but I think Baby's Days is the whole package. Register, accounting etc. I do remember a thread on FB many moons ago slating Baby's Days and how they were treated but can't remember how it ended up. I use Tapestry and think it's fab and I do know they are adding bits to it all the time so it may end up being the whole package eventually.
A quick search on here for Babysdays will bring up the past "discussions" we've had with the owner. It doesn't sound like he's changed much...
Tapestry is much easier to use and it has a very good forum you can join for EYFS advice as well. Their customer service people are friendly and polite. It has a new care diary option that is simple to use.