Pack Tactics is a very strong feature, but its real problem is that it can negatively affect how others play the game.
I've played the original Kobold race in two different campaigns. It is really good. I'm not going to labor over the specifics of the numbers, as the advantages of having advantage all the time are well documented elsewhere on the site and around the internet. Instead, I will focus more generally on what Pack Tactics amounts to when it is put into play: combat revolves around getting Pack Tactics going for the Kobold, with the caveat that it is much better for some builds than others.
First, I'll address an objection I've seen, because it will lead me into the point I'm trying to make. I have seen the comparison made between the Kobold's Pack Tactics and the barbarian's Reckless Attack feature. With a cursory examination, they do seem quite similar. The barbarian can get advantage on any attacks they want using Reckless Attack:
Starting at 2nd level, you can throw aside all concern for defense to attack with fierce desperation. When you make your first attack on your turn, you can decide to attack recklessly. Doing so gives you advantage on melee weapon attack rolls using Strength during this turn, but attack rolls against you have advantage until your next turn.
Of course, giving your enemies advantage on all attacks against you gives this feature a cost, but that cost is usually going to be offset by the barbarian's rage, giving resistance to bludgeoning, piercing, and slashing. So a naked comparison of what these features do seems to line up: they both give a character advantage on many attacks with little downsides. The argument finishes with "see, the barbarian can do it, and the barbarian is balanced, so Pack Tactics must be balanced."
But we need to be more thoughtful about our examination. In particular, one observation makes this comparison fall apart: Pack Tactics is a racial trait, Reckless Attack is a class feature. What does this mean practically? The barbarian uses a class feature slot for Reckless Attack, but the Kobold gets a whole host of class features on top of Pack Tactics. The issue is that the Kobold gets all of the features of their chosen class, plus a racial trait that functions similarly to one of the barbarians best features - it's a class feature masquerading as a racial trait.
Read through other races: racial traits generally are not particularly powerful. Unless you are playing a Variant Human, getting a free feat at 1st level (and also nothing else), combat does not revolve around utilizing your racial traits. But the problem with Pack Tactics paired with a class that makes good use of it is that it not only defines the way you play your character, its cooperative nature defines how the other player characters operate in combat. In one of my campaigns, I played a Kobold Rogue. You should already recognize the synergy - advantage for the rogue doubles the chance of scoring a critical hit with Sneak Attack. Obviously, being a rogue already gives your allies an incentive to engage in melee with your targets, but having Pack Tactics on top of it doubles this incentive and starts to redefine how your allies make decisions. And that's another reason the comparison to Reckless Attack doesn't hold up - the barbarian is going to do her thing and it doesn't change how you play your character. You will also see this same problem with Kobold Paladins (or warlocks with Eldritch Smite). A critical hit Divine Smite is a thing to behold, and playing with a Kobold Paladin means you have a strong motivation to help them make that happen.
The cooperative nature of Pack Tactics makes it a potential source of conflict. At the end of one fight as my Kobold Rogue, when discussing how things went with the rest of the party, I found myself criticizing another player for not helping me crit fish with Pack Tactics. Being a good friend, he had no qualms about telling me "well it isn't all about you", and he was right. Pack Tactics had made an ass out of me. Working together is good, obviously, but we just have to be very careful not to make others feel like they have to play a certain way in order to play into our character choices. This is, of course, a player problem at its core, but it is a player problem that is given a chance to manifest when Pack Tactics is in play.
I know we often resort to quantitative analysis when talking about how good something is in combat, and we could certainly do that with Pack Tactics. But I think the more concerning issue with the feature is not quantitative in nature; it is a design element with effects that can ripple strongly around the table. This isn't to say it should be avoided, but knowing how you might go wrong playing a Kobold could help you to avoid its chief pitfall.