I actually have looked at Battlegrounds, and found it to be only slightly better than Roll20. The way you are forced to organize tokens, maps, etc., all as separate assets within its specific folder structure--just so you can USE ANYTHING--is just a massive pain to work through on a "spur of the moment." For everything I've tried other than Tabletop Simulator, the UI is just a constant irritation. Everything is just too . . . fussy, futzy. The stuff you use the most is either buried within menu options, not intuitive, or both.
Then there's trying to resize tokens to fit the map size or grid, having to set the grid snapping on or off for both you and the players . . . it's all just too much hassle.
By comparison, once you have the basics of Tabletop Simulator down, it's truly a joy to use. It's intuitive because you're actually manipulating 3D objects, which respond as such. I love the ability to just quickly copy/paste 3D models in Tabletop Simulator. Need to throw 8 orcs on the table? Drop one down, copy and paste it 7 times, done. Need to do a quick hand-drawing of a cave complex? Pull out your trusty draw tool, draw out a few boxes, and off you go. Want to change to a different map? Right-click the game board, select a new image URL from the Web, and bam---the new map is loaded.
Want to break things up and add some slightly different terrain? Drop a few 3D models of rocks and trees on to the map, move and resize--and it doesn't take any longer to do than it would take to draw it with a dry erase pen. Basically, anything a GM can hand-draw on the table, you can recreate in Tabletop Simulator in almost the same time right in the app, once you understand how to combine pre-printed map images with the existing 3D models.
I realize it's largely preference, but nothing I've ever used besides Tabletop Simulator has really worked for what I've wanted---to simulate a battle map tabletop I could use in a live session that requires barely, if any, additional overhead from an actual battle mat.