There are quite a lot of similarities, drawing inspiration from the same titles. There are also key differences.

• BAR is able to handle more things with less or no lag (battle with up to 3K units will play lag-free and up to 60+ fps with modern (3-4 years old) hardware.
• BAR's team games can go up to 8 vs. 8 players, whereas SupCom is capped at 4 vs. 4. During certain special events, BAR's engine can even handle up to 40 vs. 40 player matches!
• BAR has several useful and interesting commands / features / options that can make playing and controlling your units easier. For example, right-click-dragging a line with a Move command will spread selected units along that line.
• BAR does not have robust transport mechanics like SupCom does—no "Ferry" command exists for repeated load/unload from a marker or factory rally point, for instance. Air transports may only carry one unit at a time. No units can fire out of a transport, or use abilities like radar jammers.
  Side note: "Heavy" air transports may lift and move certain defensive turrets, and "Light" transports can still move Construction Turrets.
• Shields don't play as prominent a role as they do in FAF. In BAR, "Plasma Deflectors" only deflect plasma projectiles, such as from LRPCs (Long-Range Plasma Cannons), and deflected shots can still hit something else—a shot can bounce right off the top of a shield and hit the base behind it!
• No "tactical missile defense" exists in BAR. Cruise missiles and tactical missiles launched from silos cannot be shot down or stopped by anything but collisions.
• BAR's naval game is somewhat more robust overall, with seaborne economies including underwater metal extractors, tidal generators, and even mobile power generation.
• SupCom (FAF) has 4 factions, with around 101 units per faction » BAR has 2 factions, with around 195 units per faction.‍
  Side note: BAR is working on a 3rd faction called the Legion.‍

By the way, if you are coming from Supcom/PA or other related game, you will probably find this guide very useful.