Battle Rifles are - together with LMGs and Shotguns - what tide me over while I (successfully) Gauss rush in b15, bear in mind this is coming from an Impossible difficulty Strict Screening user.

The trick to successful use of BR is turn economy management, squad planning, and combat positioning.

Don't replace all of your rifles with BR, do the maths on damage vs current average alien HP; overkill is wasted damage which could be traded for other attributes. Group units into "combat buddy" sub-groups that can support each other first and foremost and keep these units together on the map.

Classes that make best use of Battle Rifles are those that have access to Suppression or Flush. You rarely want to Overwatch with the Battle Rifle, instead focus on positioning and steadying your shots. Of all the attributes, Aim is the one you have the most agency over: Build bullet wizards to support your BR users, use cover destruction gratuitously and abuse the environment to your advantage, equip Scopes and consider Targeting Modules and +1 Damage items.

The most noticeable difference between running BR and regular rifles is the mission pace. It becomes a lot more tactical: slow but steady. Successful engagements with a BR squad only last a couple of turns, but you crawl across the map: two steps forward, one step back, with your point man baiting aliens into your slower moving kill zone.

Positioning really is the key to success with the BR: use elevation whenever you can afford to, take flanks, make sure your BR user has clean sight lines as to not waste steady weapon should the enemy move. Set up flank traps (retreat and hide soldiers in concealment from which they can reach flanking spots). Make the aliens come to you, not the other way around, then mow them down.

Once you reach Neural Gunlinks and MSGT soldiers, Battle Rifles become "reliable".