Which level(s) will you be playing at? I personally prefer the Barbarian class's flavor over the Fighter, but depending on level, you'll get more attacks and ASIs as a Fighter.
Overall, I'd say a Champion Fighter would be more straightforward, but a Berserker Barbarian would be more fun to play.
We typically run our characters from 1 to 20. I too enjoy the barbarian aesthetic, and it would be a lot of fun to play it as i can get pretty riled up in character.
I ask because while the fighter is more plain in rp, i feel the fighter will out perform the barb in later levels, and i am wondering if that is the correct analysis
It depends on what you mean by "outperform." Raw damage? Maybe, but it'll depend somewhat on the gear you find. Utility? Again, depends on what feats you choose. Control? Fighter, if you take the PAM/Sentinel combo (easy enough with the extra ASIs).
Both characters will be close enough in most things that I would recommend choosing whichever one you think would be more fun and engaging for you. Lv 1 to 20 is typically a long time, and combat will only be part of that (I assume).
I would also ask your DM about whether they'd have any table rules about the Berzerker fatigue thing. If they'd rule it RAW, I'd recommend a Totem barbarian instead. Bear totem at Lv 3 makes you feel like an absolute beast, IMO.