I've only used Annie Sloan chalk paint before, so I definitely was comparing them as I painted my desk. I haven't done projects in similar colors in each brand, so I won't be able review that, but overall quality and difference I can review.
As far as wax for the two brands, the difference is night and day. Annie Sloan's wax is just that - wax. It has the feel of petroleum jelly that you can literally scoop up and wipe around the piece. And ASCP's wax has that smell of chemicals - you know what I mean, the same smell varnish and polyurethane and other protective things have that are anti-water.
With Waverly's their "wax" is liquid, not wax, and has no chemical smell. Sad. That smell to me tells me my furniture will be protected and the paint will stay in place. I had to use a paint brush with Waverly and paint some wax on, then use a cloth to rub it all around. Thankfully when I was all done with the wax of Waverly, it felt smooth and nice and waterproof just like with ASCP, but maybe not quite as nice. Definitely don't use this wax on something that is going to have a lot of wear on it, or consider using a different top coat entirely. (polycrilic, polyurethane - google it for your particular use and piece)
For the paint itself, I found them VERY similar. In fact, Waverly's might have had an even thicker and better texture than Annie Sloan. Waverly was thick and creamy and was actually enjoyable to paint because it was so easy and the coverage was so amazing. Annie Sloan's was creamy, but not THAT creamy. Still great coverage though. Like both paints are going to give you at least 3 small projects use of just one quart. Don't quote me on that. I still have to do 2 or 3 coats with each brand, but that's just pretty much par for the course with chalk paint.
To add a little more storage, we got two 43 inch floating shelves from Ikea. Normally, I hate open shelving because I have the worst organization skills known to mankind and I don't want that mess to be "open" to the world, but this is far enough out of the way, and we just installed a couple of legit cabinets in the laundry room a few weeks ago, and installing those is not for the faint of heart, which I definitely am, especially since I've been sick this week :/.
Here's a look at my definitely staged cabinets, hopefully the actual organization will take place soon??? We got the boxes and faux purple plant from Ikea, Nick's Grandpa Allred made the white shelf (so darling) and I found the white framed art at Kirkland's and literally couldn't not buy it (double negative much?) Let me know if you like it and I'll love you forever.