My Destiny impressions
http://arcademy.net/forum/index.php/topic,416.msg3285.html#msg3285
Activities
There are various levels of activities with various intensities, but only 4 are in the alpha:
Social - zero intensity. This is the City under the Traveller. Here you will find all of your vendors and mentors, and where you can hang out with other players. When you're here, you put your weapons away and walk around in third person.
Free Roam - light intensity. This is the ODST-overworld esque portion of the game. You can explore the earth above, caves, buildings, and mines. You can pick up mission beacons while free roaming and complete MMO-esque quests like collect X amount of material, or wipe out all the enemies in an area. You don't have to turn them in, it just completes once you finish and dished out rewards.
Strikes - guided missions where you go after a boss or big bad and take them down with 2 other friends. You can select Brave (Heroic) or Legend (Legendary) difficulty when doing these activities. On Legend, enemies are relentless and do not care for your hiding attempts. They'll persue you on Brave, but on Legend, expect to be managing your resources carefully. You also take an armor and attack damage penalty (percentage wise) on Legend. Currently it's something like -59%.
The Crucible - multiplayer. Works like Halo in that there are playlists to choose from. The only one in the Alpha is Control, the familiar Land Grab gametype from Halo.
There are more activities in the final game, including Raids which are 6-man and will require team coordination. A Bungie employee I asked said the intent for Raids is that even experienced players will feel the heat.
How the persistence works
When entering a free roam, you are put into an overworld-esque area. The overworld is divided into invisible "bubbles", and bubbles allow up to 6 people in them at once in each instances. So I can be free roaming, and a fire team can go by me on their way to a Strike, they'll go around a corner into another bubble and they're seamlessly networked into the Strike bubble and out of mine. No hitches or UI text saying someone has left or joined. Note that only people in fire teams are kept together - if you cross a boundary of one of these instance bubbles with a pubby, they'll just blink out of existence. You don't have to worry about griefers following you into a mine for loot.
If you're not paying attention to how it's managing instances though, what you get is the impression quite a few Guardians are roaming around in this world, and it's seamlessly instancing people in and out of areas to give you people to interact with.
Public Events
While free roaming, you'll also see Fallen drop in with their ships and some sort of hardware or troop platoon. The neat thing about public events is you can watch a fire team do them from afar - you're not forced to participate in them. If you wish to join, you simply run up to what's going on and the game will tell you that you've joined a Public Event. Now you can help other Guardians complete it. It's nice and seamless.
Multiplayer
Multiplayer is somewhere between Haloish and Callofdutyish, more of the Halo side of things. Your character from single player carries over, weapons and all. The playlist in the alpha has "Level Advantages" turned off, so no idea how those play out yet. Ironsights are here (sigh), and you retain your super ability. The movement has that Halo style weight to it. Kill times are not quick like Call of Duty, though, and you cannot quick scope. Autoaim seemed fairly low, although I did see aim friction when big threats passed in front of me, like vehicles.
Supers can be activated once you have enough Super charge. They have a lot of wind up time so you can see someone super charged coming at you, but the playerbase should be keeping their eye out on this and Bungie should be keeping an eye on balancing these for multi.
Also, on big maps like the Moon, you can summon your vehicle like you can in Free Roam. Unlike Free Roam, however, your vehicle has limited boost energy.
Sidenote: Melee doesn't work like Halo or CoD, in that back stabs are instant kills. It's two melees from ANY direction, so far.
Weapons modify your movement speed, although i only notice the Heavy weapon slowing me down when it's out. No idea of other weapons will do the same.
Interestingly, you can use your emotes in multiplayer. So you can dance, sit, wave and point while shooting mans. I forsee a lot of dance and sit-taunts in the future.
Criticisms: Multiplayer
Destiny has adopted elements of Call of Duty's "rich get richer" gameplay, not all of them, but some of them with PvP, which i'm just going to call multiplayer at this moment. Since you bring all your weapons over to multiplayer, this means you spawn with a shotgun. Or a sniper rifle. Or a rocket launcher. Or a chaingun. They attempt to balance this with the fact that you only spawn with ammo for your primary gun, but I still ran into people just sitting on the outside ring of the moon map and sniping. And since they spawned with it, they could just go get the ammo off their dead body and resume sniping. I'm deeply concerned about this choice, and am thinking I might not be playing PvP for too long if they keep it this way.
Currently, you have to pick ammo up off dead players, or ammo crates. So the heavy ammo crate might be in the middle of the map, and special ammo will be on the sides, but it gives you so much ammo that you'll mostly stay supplied for the rest of your life.
They need to either give you way less ammo from the crates for the special and heavy weapon, or make you acquire your weapon from the crate. This would make it so only one team member can have a power weapon at the start, instead of.. everyone.
The Interceptor is a Scorpion/Wraith like vehicle on the Moon map. It needs to be placed like one, not given to you as easily as it is.
Strafing seems a bit slow.
There should be an option or the presence of a playlist in this game where everyone starts with the same weapon for some pure shooting action.
If you were looking for this to be secretly a renamed Halo, look elsewhere. It's familiar, but it's not an arcade shooter. It's an RPG shooter. (Not actually a criticism, just an observation)
Criticisms: UI
Most of Destiny's UI is driven by moving a virtual mouse around the menu. This has upsides and downsides. It's handy for managing the huge grid of items and weapons and armor vendors may have. But in some areas, it's overkill. The Orbit menu, for example, has buttons just in the corners, far away from each other. I wish I could just use the dpad in these menus to navigate or quick-snap the virtual cursor to the buttons. Some buttons and boxes seem to have a bigger hitbox than they look, so I have to move the cursor a lot more than I expect in some spots to select. Hopefully this UI decision is refined.
Of note
The entire time I was playing the Alpha, Bungie employees would ask me and the other community members playing what we didn't like about the game. Even when you tried to compliment them on features above, like the seamlessness, they'd steer our conversation back to what we don't like. They're taking the feedback very seriously and are being very humble about this game. In a previous alpha, I left a pretty harsh but constructive post on their alpha forums, along with some other people about certain things. A lot of them were addressed in this alpha. I truly believe they are taking what they hear from First Look and the Public Beta very seriously. Some of the stuff mentioned above has been talked with directly with employees that are in charge of it, and they're looking into certain changes already. They really do want to hear your (constructive) negative feedback on the game. Please share your critique with them in the Alpha and Beta.
Also, the game supports clans. Just thought I'd throw that out there.