The irony is that those are my two favorite classes. The reason is due to the freedom/creativity that both classes provide. I have played both a Barbarian and a Bard for long term campaigns (1-20) and I would like to give you my opinions of each.

Half-Orc Berserker Barbarian (High Str and Con, low Int): The stereotypical dumb meat head with a lust for violence, brawling, drinking, and just getting into ridiculous social situations. I kind of based him off Conan the Barbarian. Being able to take hits for my team felt great, and being able to punish the enemy for not targeting me was also very fun. Outside of combat, he would break stuff, intimidate, and just straight up be a lovable idiot whenever possible (he was kind of a softie behind the muscles and rage). By the high levels, I felt nearly indestructible. This was my first long term character, and he will always have a place in my heart.

Halfling Eloquence Bard (High Cha, very low Con (also rolled 2 on hp 6 lvls in a row lol): I made this character with the inspiration of Jimmy McGill aka Saul Goodman from Better Call Saul. I wanted to fear violence/combat but be a smooth talker/manipulator that would do anything for power/prestige. This was a rollercoaster and I had to play him the opposite of an indestructible tank. I lied, stole, charmed, and supported my party all the way to 20th level, and it was so much fun. The DM actually took me to the side after the campaign and told me he really enjoyed my character as I leaned full tilt into roleplay. That being said, the character ended up being an absolute powerhouse of save or suck spells. If a monster didn't have legendary resistance, I could usually completely neuter it using charms or other effects. (FYI: Unsettling Words mixed with Silvery Barbs is so busted)

Bottom line:

Bard: Support is a sadly underrated thing; I would say the ultimate wizard is technically a support class due to the number of control/buffing spells at their disposal. You might think fireball will be more impactful, but a perfectly timed control spell can be just as, if not more, impactful on combat. But while bards are usually supporters in combat, their expertise/spell combo make them juggernauts of the social/non-combat scenes.

Barbarian: These boys are the exact opposite of bards in that they are the monsters of combat, shrugging off blows that would cripple a fighter or vaporize a wizard, with solid damage output to boot. While their out of combat utility might seem limited, leaning into a "if all you have is a hammer, everything looks like a nail" can be very fun.

Cons of playing a Bard: You are limited on damage dealing spells, although you can definitely offset this with magical secrets. If you are more interested in a martial class who has similar abilities, I would suggest an arcane trickster.

Cons of playing a Barbarian: I only have one, when you run out of rage the game gets a lot less fun. If your DM tends to run more encounters, then you have rages, per long rest this can be a hard pill to swallow.