Want to give a longer form of impressions for strictly the PvP side of the beta. I think PvE and PvP are truly separate modes that deserve separate critique, and as someone who derives much more fun -- in the general -- from PvP than PvE, I'm probably ill-equipped to speak to how things *should* look there. Suffice it to say, I played the strike and story mission and enjoyed both, and do feel there are some issues there, but I think other people are tackling that well enough.
PvP in Destiny 2 just seems like a *reaction* to what Destiny 1 multiplayer was and became over the years. In Destiny 1, things were, well, chaotic. Certain exotics circumvented established 'rules', like the special economy. The 6v6 modes were laggy, chaotic, and became more about combinations of abilities and gear that allowed you to reduce cooldowns to almost non-existent and spam those abilities. It wasn't just possible to be a God in Destiny, in some cases you could nearly become untouchable if you had the right set of gear, the right personal skill level, the right area to run about in. Everything was powerful, even though everything was nerfed. A well-placed headshot with a good hand cannon rolled smoothly into a single melee that would decimate any player in < .4 seconds. Whole groups of people could die so fast that they very literally would have no clue what hit them. In the 3v3 modes, things were a bit better, a bit less chaotic, but people attempted to climb to the top by being even more adherent to what would work the best: sticky grenades for an easy one-shot kill, regenerating ammo sniper rifles for long distance, and hand cannons that had a chance of being able to two-tap another player. Supers would clutch entire games, turning things into a chess match game of waiting/camping rather than anything else. Even though 3v3 was better, it wasn't much fun, not in the last moments of its life (which people are entertaining now).
So enter 4v4. It's inherently less chaotic, and I'd suppose a lot less laggy by my personal experience, but the reduction of insanity doesn't end there. Now people don't really play to ability spam, because cooldowns take a long while. Instead of going for "random" grenade kills, most people will wait and play those rarer resources when it is liable to make a difference. Everyone is stronger, while everything else is a bit weaker (it's kind of hard to parse the difference here -- are we all stronger, or are the weapons weaker, or a bit of both?). Certain problematic grenades don't one-shot anymore. A two-tap weapon doesn't seem to exist. Melees take a minimum of three hits on a full-health player to kill. Most fights, unsurprisingly, are gunfights now. Players move slower, a lot slower, with only some abilities to reduce their chance of dying -- not to increase their chance of killing. It's a much decisive, calculating affair, with maps pulled into to a reasonable size to support 4v4. The lanes are thought-out, with their own pros and cons for use. In Countdown, the objective basically forces teams to play the game, rather than camp or wait for supers that take a *long* time to come, even when you're playing at peak capability. Teamshots are more important than any super, and teams working together intelligently win games, not solo heroes of the crucible.
It's a big change. Huge, for a Destiny player familiar with what they're looking at. It's going to piss a *lot* of people off, for one. People who have grown use to the non-sense of Destiny 1 (Characters who, with the lowest possible agility stat, are faster than any class, for example). Of course, we aren't seeing the whole picture yet, and exotics / armor combinations may change up a bit of how this game plays, but assuming that there isn't a big difference between this and release, Destiny 2 is going to ask people to adapt to a new kind of PvP experience. One that is less about *you*, and more about you and your friends, together. It's a breathe of fresh air for me. The two primary system especially gives you more flexibility without making you necessarily more powerful; tackling one of the long border lanes of the Countdown map means you'll want a powerful scout or pulse rifle on you. Going straight down the middle to figure out if the opposing team is split up? You might prefer to pull out your hand-cannon for a close-range fight if things go wrong. It's an element of choice that works well for PvP, without disturbing the distribution of power for players.
If you're the kind of player who likes to clutch games, your biggest option is the power ammo pickups. In a particularly nasty game I played with my team, everyone was dead, and I scooped up the power ammo loading it into my shotgun. I carried two rounds doing this, killing the entire enemy team. It's an unlikely feat, only made possible by those other players not being too good -- but the potential to have great plays is here, it's just much harder and requires strategy.
All of this, I think, is great for Destiny PvP. I have yet to get bored of either Countdown or Control, and I think these maps are just beautifully designed for both. As far as PvE is concerned... that is a whole other thing, and as I've read the carefully described critiques here, I find myself agreeing with many of them. I sincerely hope that whatever changes are in store for PvE don't find themselves in the PvP too much, as the balance is close to perfect in my mind, but certainly some simple things like tweaks to guns, slight cooldown reductions, are reasonable.
EDIT: I want to add one other thing here. I'm decent at Destiny 1 PVP, and when I want to go flawless in trials or something I will play with two friends who are above a 1.0 kd to do so (we range from 1.3 playing level to like 1.8 kd, myself being the lowest of the three). What the new KA/D system does I think is brilliant, because a lot of the time I just want to play with friends and not care about their personal skill level -- what I'm finding is that people I play with who had trouble breaking past a .7 are loving seeing their contributions to the team noted; they don't have to stare at small numbers anymore that remind them they die more than they kill. Instead, they are seeing a more comprehensive collection of their contributions, and because of it, even when we lose, everyone is having more fun. Team shotting makes such a huge difference here that even players who on their own could do next to nothing in D1 can actually significantly contribute in D2. I'm loving that many of my friends who aren't as good as myself at these kind of games are feeling like they can contribute more. So the KA/D system gets a big thumbs up from me. I'm not good enough to carry anyone to the lighthouse in D1, but in D2, with connection-based instead of win-based matchmaking, and matchmaking with randoms, and the 4 instead of 3 person groups, I can see me and my better friends being easily able to take friends who aren't as good to whatever D2's lighthouse is -- people who never got to see it in D1. That's going to put a smile on my face, when it happens.