Started a new project and decided to go full ConstraintLayout. I figure it is the future so I might as well use it. I used AutoLayout when I was doing iOS work so I have the general idea down.
First off I am using 1.1 because it has Barriers, Guides and Groups. To properly replace TableLayouts you need Barriers. This allows you to say "Hey, here are X controls, I want an edge to be based on the longest one". This is what happens with stretched TableLayout columns. It also means your layout will adjust if you change text label widths which can easily happen in other languages. Trying to stay on top of the internationalization game.
Group is nice if you need to hide a group of controls which you may need to do if you have a Switch that toggles visibility of a number of items.
Guides allow you to do percentage layouts. This gets rid of that deprecated layout.
Now my layouts are nice and flat. I went back to previous app and converted most of those layouts as well. The conversion tool in Android Studio is hit and miss. If you have just a RelativeLayout it will probably do a decent job converting it but you may have to set a width to 0dp here and there as the control may be set to start / end against another control but have a width of match_parent.
I also find you have to put in spacer controls at the bottom of some layouts, especially row layouts used in a RecyclerView, as the bottom margin is ignored for the lowest item in a layout. Did not cause too many issues.
I recommend you give this a shot as well.