It's open world in the sense that you can explore huge locations with others, doing infinitely generating quests, along with some randomly-appearing community quests as well. You can travel between these giant locations via a starship. 

From my experience, I never felt confined. 

I was not hyped for this game, because it's another FPS in a very crowded and saturated market. And I didn't wanna fall for the hype (you know....$500M ad campaign) just to be disappointed. And on top of all that, pre-alpha previews were saying this game was 'meh' at best. But man, after playing the Alpha, I'm gonna pre-order it, in lieu of the beta. I, now, can't believe there was so much hate for the game on the MS fan side of things (I saw some comments like "Sunset Overdrive looks great! But will Bungie please add some fun to Destiny?). I think I get it: Destiny is getting pushed for PS4, so it needs to be downplayed on that side (and talk up every XBone exclusive in the meantime), but you guys get the game too! It's not like just because it's being marketed for the PS4 that it isn't on the XBone, 360, or PS3. It's like a mix of Halo and Borderlands, two of some of the best franchises in recent memory. What's to hate about that?!

I don't know what improvements Bungie is going to make, but if I could do all the stuff I did in the alpha on ONE planet, just imagine what else is in store. I'll keep my hype and expectations in check, but I am now, officially, looking forward to the game. All I needed was a reason to, beforehand, and the alpha alone delivered that reason

Is the gameplay similar to or better than  Halo ?

I completely agree. I had this game pre-ordered a while ago, but because of the recent content Activision put out I was losing interest. The Alpha though was just amazing. Destiny is easily my most anticipated game for 2014 now.

MUCH better. For one, you are no longer confined to carrying only 2 weapons. You can also customize your gear to suit your needs, which allows for a lot of personalization. Gameplay is no longer running from point A to point B, you now have dynamic missions that are actually variable. I haven't played the the PvP multiplayer too much, but from what I have it's also lots of fun, and very well balanced. 

Also, there's a class that can use magic. MAGIC. That alone makes it better than Halo, imo.

Hearing mixed opinions about the alpha so far. From the typical fetch mmo quests to "kill 10 enemies..." which actually begin repeating after a while as well as the poor and uninspired voice acting and public events being different variants of the same thing. Halo reach was a step in the wrong direction for them when it came to multiplayer and instead of listening to their community they have chosen to go down that path for Destiny's pvp. This game might end up being good but its quite evident that it won't live up to the hype at all.

I trust your judgement because most players I ask the same question they give the same answer.I now persons who hated the game and they are pre ordering it now.

There are no "kill ten enemies", but there is "collect item drops from a certain enemy", like I mentioned in the OP. There are also random boss events that spring up, exploratory events that ask you to scout out areas, along with entire missions akin to dungeon raiding, were you go in with 2 or 3 others and hunt down enemies, look for loot, etc. all while try to reach the end of the dungeon. 

The VA is average, but there wasn't much to judge on. PvP, from the little I played, was still pretty fun, better than Reach or any of the other Halo games, especially since you can customize every bit of your equipment (and the game balancing is done very well). Overall, no one can tell exaclty what it will be like, but after playing it, I'm already impressed, and eagerly awaiting the beta.

So "collect 10 item drops by these enemies..."? Same thing. Customization does not equal a better game and never will but to each their own.

To each their own.