Sneak Attack is better than you think

In order to land a sneak attack, the rogue needs to be making an attack with advantage, or the target needs to have another enemy within 5 feet (and that enemy isn't incapacitated, and you don't have disadvantage), while you are using either a finesse or ranged weapon.

This sounds kind of tricky, but let's look a little closer. Firstly, a rogue is almost always going to be using a finesse or ranged weapon. Rogues often have a lot of dex so finesse is great for them, and ranged weapons will keep the rogue out of harm.

In a party there is usually at least 1 other melee character, so the rogue will always have a guaranteed source of sneak attacks just by hanging around them.

The rogue can also use their bonus action to hide (rogues often have high dex, so hiding is no big deal), giving advantage and sneak attack. The ease of accessing both advantage and sneak attacks is what powers many rogues.

In combat a rogue will almost always sneak attack for every single attack. What's more, the rogue could even do this more than once in a round, by using opportunity attacks. Even if the rogue didn't have sneak attack, they would probably still be hiding to gain advantage, and working together with other melee characters.

Psychic Blades is worse than you think

While the rogue is out there spamming sneak attacks, the bard is a lot more limited. Firstly, they are limited by their number of bardic inspiration die. With 20 charisma the bard only has 5 uses per rest. That's great if you have 1 fight per rest, but otherwise it's extremely limiting. What's more, if you use your inspiration die for damage, you can't use them for, you know, inspiring people.

Psychic Blades also does not scale as nicely as sneak attack, which isn't a big problem but it will mean that half the time it's dealing less damage.

Bards don't have a lot of feature support for melee combat either. They don't have cunning actions like rogues, and they have to split their attributes between cha and str/dex to be effective. That tax and lack of feature support makes them less effective. Even if they had access to sneak attack, rogue would be superior.

While psychic damage type isn't commonly resisted, a rogue can equip a magic weapon and bypass most physical resistances. By the time this becomes a problem, the rogue probably already has the solution.

Good in Tier 1, underpowered in Tier 2+

No Heckling

This feature doubles the amount of disadvantage you can hand out on turns where you'd normally just cast a cantrip. It also allows you to make a weapon attack and still throw out vicious mockery. No Heckling is quite strong in Tier 1, but less interesting in Tier 2+:

• Monsters usually scale by adding more attacks (rather than a single big attack). This makes vicious mockery fall off in usefulness as Multiattack enters play.
• Weapon attacks from non-martial bards also fall off rapidly, often replaced by 1st or 2nd level spells (which prevent you from using No Heckling). At level 5, would you rather shoot a crossbow for around 6 damage, or force a Wisdom save for 10 + an opportunity attack from the barbarian (via dissonant whispers)?
• Bardic Inspiration competes for a bonus action, particularly at level 5+ when it recharges after a short rest.

Laughter is Contagious

Tasha's hideous laughter is a decent hard control spell for Tier 1 bards, mostly because it's the only generic one. Monster HP rapidly outpaces sleep. Hold person requires the same save for a much more lethal effect, but only works on humanoids. Suggestion has a ton of caveats and DM discretion.

Doubling the number of targets is a big boost to the spell's effectiveness, though the 5 foot requirement is highly restrictive. An upcast hold person requires that all targets be within 30 feet of each other and I frequently find that generous restriction too limiting.

And now for the elephant in the room: at level 5+, a twinned Tasha's hideous laughter needs to compete with fear and hypnotic pattern for concentration. This problem only gets worse as the number of spell slots increases. By level 9, the bard has seven spell slots of 3rd level or higher, many of which will be used for concentration spells.

Can't Stop Me

I just don't see this coming up very often. Even if it does (and you can't simply move out of the radius), hypnotic pattern is a fantastic spell that doesn't require verbal components.

You're Killing It

This shares shortcomings with Laughter is Contagious. You have to forgo hypnotic pattern and fear to use this, and I don't see it being worth the trade-off.

Tough Crowd

The first bullet point of this feature means Countercharm is actually usable! There are very few anti-charmed/frightened effects that protect an area. This won't come up every session, but when it does, it'll be extremely useful.

The second bullet point may have some out-of-combat issues. Countercharm has unlimited uses, so you could spam the Charisma save against a captured creature until it failed. The creature would then be indifferent until the bard got bored of using Countercharm. I would recommend granting a creature immunity for a minute (or an hour) on a successful saving throw.

Laughter is the Best Medicine

This seems fine. It's comparable to a Life cleric's Disciple of Life - lower level spells heal more than Disciple of Life; higher level spells heal less.

I'm on a Roll

Infectious Inspiration is a powerful (but balanced) feature for 14th level. This feature and Laughter is the Best Medicine certainly improve things, but the earlier features are rarely used at this level, leaving the subclass underpowered overall.

Potential fix for Laughter is Contagious

At higher levels, Tasha's hideous laughter must compete with fear, hypnotic pattern, and other fantastic spells for concentration. This is a critical balancing feature, preventing buff/debuff stacking. However, a single-target control spell with repeated saving throws might be weak enough to justify the following feature (replacing Laughter is Contagious):

When you use a spell slot to cast Tasha's hideous laughter, you can expend one use of your Bardic Inspiration to change its duration to 1 minute for this casting (no longer requiring concentration). When you do so, any other instance of Tasha's hideous laughter that you have cast using this feature ends.

This effectively allows you to target one creature with Tasha's hideous laughter without requiring concentration. You still get something like a twinned effect over the course of two turns, since you can cast the spell normally (with concentration) to target a second creature.

Anything that removes concentration should be watched closely for balance concerns, though I believe that this spell and feature have enough built-in caveats to keep things from getting out of hand.