Before ditching Picasa, remember what it is for - organising and editing the files ON YOUR MACHINE. The reason that it is being sidelined is that Google, along with Apple and Microsoft are all about getting you to use stuff online. If what you want is to organise the stuff on your local drive with editing capability then stick with Picasa. It's a mature product that has nowhere to go developmentally, it works. The best paid alternative is Adobe Lightroom.
Google photos is all about pushing stuff online, IMO they are making a reasonable fist of it, I expect the next six months to add a degree of usability that will improve it, the current feature of searching your photos for objects and things is on the amusing side of awesome (eg, you can search all your photos for "bicycles" as if you had tagged them). I'd wait a while before making any organisational changes to see what happens.