Never used SAI. How would you say it's an improvement over Photoshop?
The ecosystem in Paint Tool SAI is very simple and straight forward and it puts all the things you'd need right in front of you. This means that less time is spent navigating menus and learning the software and more time is spent painting. It obviously is not as robust as Photoshop, but it has more than enough tools I'd be using for the style I'm going for. I feel like my drawings take form and come to life sooner in SAI, which helps me to better visualize and create them. If I require additional editing, I can export all the layers into a .psd and touch it up in Photoshop.
In that way, SAI is essentially "Photoshop Lite", only streamlined for 2D artists. The water color options make for good paintings too, which is what I was practicing above. With Photoshop, it feels like I'd have spent twice as long learning how to do that and half as long figuring out what option I had turned on/off that was preventing me from painting. SAI's quick learning curve was a tremendous encouragement in that respect.
It still has layers, groups, folders, and most of Photoshop's tools; however, you'll definitely be missing some things if you start with or switch to SAI. It doesn't have a polygon tool, and I've grown quite fond of Photoshop's Smudge tool, which is absent along with some of the other intricate ones. But again, that .psd option helps if you want to give things a once-over with a larger toolset before you finish.
I'm not sure what else there is to say. SAI just makes drawing fun, even if I'm scribbling something. And when I'm having fun instead of being frustrated, it motivates me to keep at it and get better.