So, I have found the All-American, which is probably my favorite gun in the game and I use it in all my guns playthroughs. But this is my first playthrough with GRA - the Bozar also looks extremely cool, and the stats look alright. I don't want to buy it and then use it only once though, since it's extremely expensive. So I guess my actual question is, is the Bozar worth it, if I already have the All-American?

I would say no.

The Bozar is a confused gun that can't really figure out what it wants to do. It's an LMG that does less damage in exchange for range, but it's spread is pretty high for sniping.
As an example, I recently uploaded this vid to show off the Sprtel-Wood 9700, and at a couple points I "snipe" with it: http://www.youtube.com/watch?v=-1ts_TVi-3w

The Sprtel-Wood 9700 has a spread of .5, the Bozar is like .75. Also worth mentioning that I BELIEVE that character had Trigger Discipline, so there the Sprtel is even more accurate than .5.
But yeah, basically you can watch and judge for yourself if you think the accuracy is good enough or not. Things to remember though are that the Bozar is slightly less accurate and does much less damage, so....In my opinion you just end up alerting a swarm of deathclaws and not killing them nearly quick enough, whereas you COULD'VE just used a sniper...And if you say "ok well I'll just use the Bozar for close range," well then the LMG is superior to it...

I really don't think so, I was disappointed with the Bozar when I first for it because like Longknife said its a gun that doesn't really know what it wants to be, I'd pick the All American over it any day.

I see, I see. That's a real shame, since the Bozar looks frickin' awesome. I'm a long- to mid-range sniper by default so it was a pretty poor fit anyway. I'll use that 20+k to get Paciencia or the Medicine Stick, I guess.

On paper it seems like the Bozar isn't really that inferior to the LMG (lower spread, lower clip size, slightly higher DPS, about the same crit rate and dmg), but I suppose it's something that's experienced in play.

Save your game, buy it and then test it out in a combat place like infront of the fiends vault that keep it if you like it or load your old save if you don't.
it's great as a sort of assault rifle.

The Bozar is quite formidable in its own merits.
As for all Auto Weapons, the Bozar is not exactly ammo effecient, and it using a semi-scarce type of ammo doesn't alleviate that, too.
Bottom line, the All-American is for sure the more versatile, all purpose gun.
But that's not the Bozars fault, it is that they made the All American that strong of a package.
However, the Bozar has some mood points on its own. If you use it with Match Rounds, the spread will actually become managable.
It still is not on Sniper Rifle levels, but you'll hit your targets, and you'll hit them hard. The RoF doesn't leave anything to be desired.
It is a scoped LMG, after all.
Also, it comes with extremely low AP costs for its class, 19 iirc, which qualifies it as a life insurance, too.
As a crowd control tool, there isn't that much that actually can keep up with the Bozar, or even surpass it.
Pacienca and MS are catering to different needs, so keep that in mind when thinking about widening your portfolio.
You can have the Gobi for free, which fills in the same role as Pacienca and the MS.