First I see a lot of people raving about Circles and how they change everything. I'm not sure I get it. Facebook has had user lists and a privacy setting on each status update for quite some time. I personally use a few lists on Facebook to share stuff with different sets of people. I have lists for people I know through Cub Scouts, people I know through church, people I went to high school with, people I work with, etc. Some of my Facebook friends are in multiple groups. So when I post something that would only interest one of those groups, I can filter my post so it's only visible to just that group. That's just like sharing to a circle on Google+. I can also share a post with everyone except a group of people, which is something Google+ lacks so far. Facebook does let you share a post with "friends of friends" and "everyone" so posts can be visible outside of your friends list, but there's no way for non-friends to see them unless they go to your particular Facebook profile. So Google+ clearly does a better job of sharing posts with the public (people outside of your network). Facebook's friend lists aren't that hard to manage, but the Google+ circles UI is a little nicer. It takes a little more work in Facebook to set the privacy / visibility of a status post than in Google+, but I think it's 6 clicks and typing the list name vs. 2 clicks and typing the circle name so it's not a huge difference.
Twitter on the other hand has no outbound filtering at all. Except for making your entire Twitter stream private, you can't send a tweet to anyone except all of your followers (and anyone that finds it through searches). So for sending stuff to limited groups of people, Google+ clearly beats Twitter, but Twitter doesn't even try to handle that.
The inbound side is where Google+ really shows something different than Facebook. You can pick all of your circles at once or select individual circles to view posts from people in those circles. Unfortunately there's no way yet to pick more than one circle at a time or all circles except one or two. I swear Facebook used to have the ability to select friend lists to see updates from just friends on each list, but I can't find it in the current UI. So that's clearly a win for Google+.
Twitter though has a lot of flexibility on the inbound side. Even with the base Twitter web UI, you can set up many lists of Twitter users to organize different streams. You don't even have to follow the people that are on your lists. You also get the choice of making each list public or keeping it private. I have both. For example I have a public list of Tampa media people and media outlets. It's too much for me to follow regularly, but when something newsworthy is happening in the area, it's a great resource. I also keep a "catchup" private list of the Twitter accounts that I really want to keep up with. So whenever I don't have time to read my entire Twitter feed, I scan just my "catchup" list instead. (Lately that's all I usually get time for and I almost need to create an even shorter list for when I'm really short on time.) I also have some other special interest lists I can look at depending on my context. For example I have one for a bunch of work-related Twitter accounts and another for one with a bunch of scouting-related Twitter accounts. So in my mind Twitter gets a slight win over Google+ on the inbound side, mostly because you can publish lists publicly for others to use.
Second, I've seen people raving about how Google+ handles conversations a lot better than Twitter. I'm not sure. It is true that I get to see everyone's response to a post in Google+ but that's not always a good thing. With my friends and posts that get a few responses, it's great. When Scoble or Gina Trapani posts something and gets 200 responses, it's not so useful. There's sort of a up-voting because people can +1 a comment but there's no way yet to hide comments that haven't been up-voted. But on Twitter you don't automatically see responses to posts other people make. With most clients, you won't even see @responses from the person you're following unless you follow both people in the conversation. So I guess I'd say it handles conversations differently and lets you see more of them, but I'm not sure that it's a good thing. It seems almost identical to Facebook's conversations though. I guess the only big difference I can see compared to Facebook is that on Facebook, you can usually post on another person's (or page's) wall and start a new conversation. It sounds useful, but for highly followed people and pages, it's just a lot more noise.
Third, people are really liking the "hangout" video chat in Google+. I have to agree it looks pretty good and quite useful. We use video chat for work through Skype and WebEx so it's not very ground-breaking to me, but I certainly see the value. It does have all the problems with every other video chat, the biggest of which is that a lot of times people just aren't ready or willing to go on camera.
I really haven't been able to try Huddles which is a group messaging piece available from the mobile apps. That was a key prospective use for Twitter early on - text messaging among groups of friends rather than one-on-one. Twitter users moved on pretty quickly from that and today I doubt that very many tweets are delivered over SMS.
I've tried Sparks on Google+ but I don't really get them. It's a bit like a weak RSS reader or news alerts. Some of the topics I tried are filled with useless and irrelevant results but some of the big topics do OK. But I don't think they'll catch on at all in their current form.
I've seen more than a few people say that they're done with Facebook now that Google+ is here. I don't really see that happening for me. I currently have quite a split between people I know on Facebook vs. people I know on Twitter. On Twitter I follow a lot of people I don't even know, but out of the people I do know, they're mostly more technical than my average Facebook friend. So if I want to share some geeky link, it has to go on Twitter. I might stick it on Facebook but I can expect that 70% of my Facebook friends won't care. So far almost every person I interact with on Google+ is also fairly active on Twitter. So I don't see it really making much of a dent in Facebook. It could take some people away from Twitter though. I have noticed that essentially the same post on both Facebook and Google+ is currently getting more comments on Google+ but that's likely just the novelty factor.
There are clearly some issues to resolve in Google+ and a lot of possibilities. Google is quite good at iterating quickly and isn't afraid to roll changes into a product, so this will be interesting to see Google+ change rapidly.