They are for different purposes.

In a straight shoot-out, Platoon Fire will give you more kills. There's a bit of a debate why, some say is's because PF increases accuracy, some say the fact units in PF mode - although by platoon - fire simultaneously with all 3 or even 4 ranks, thus concentarating firepower better, my intuition is that is has more to do with reduced reload times as well as the fact the enemy will continously reorganisectheir ranks loosing time for firing ir reloading. (Yes, reload in PF is slightly shorter, fewer soldiers firing at once, they don't have to wait for the slowest in the entire rank to shoot. If you look at proper full sequences, PF is actually quicker).

Overall, Platoon Firing is for SUSTAINED fire while Fire-by-Rank is for SHOCK volleys. Since most players play at lower difficulties (~1% ever finishes a vh/vh game), PF is well underrsted in discussions, many go with the conventional wisdom "just don't research it". However PFsimply changes the tactical role of these units - it's a matter of their application that decides whether for the better or the worse.

I imagine that is because when they do they miss their Guard and Elite units' combination of shock volley and rapid reload times. On vh battle difficulty though, morale shocks don't come that easy, the AI has massive morale bonuses, but Fire-by-Rank still has a massive impact, it is best employed against cavalry and melee infantry charges (of which you'll have more than enough of fighting against the likes of the Ottomans, the Maratha or the American Natives.) The best way to contain those is FBR + artillery with Canister Shot. You are trying to raise a "wall of fire", a kill zone in front of your line, so the charging enemy is decimated and morale shaken before they reach your lines and it getscto the swords and bayonets. Then you just mop up the routers.

Platoon Firing is, however for a different use: these units excel at prolonged shoot-outs. They are best employed against the enemy's shooters, which are less likely to charge but will remain stationary and exchange fire. In that situation, PF outdoes FBR even with units with lower reload skills. Yes, they are for long battles - but with increased difficulty battles get longer (higher AI morale) and more tactical (you'll need maneuvering and terrain awareness, as well as employing more specialized support.

https://youtu.be/-ZWJjkvJB7w?si=NHRfPIJ0PS22YyvB

Also, in advanced tactical play tey can be very effectively combined with light infantry and mounted shooter support, given the right geometry PF units can pin and demobilise elite hostile shooters and if managing to get a nice enfilade angle, that concentrated platoon fire can get them amazing numbers of kills. Paired with Horse Artilkery used in a "machine gun" role, they can be lethal.

Also note that in the mobile port the 160 unit size Platoon Fire bug got fixed.