You no longer have to wait for an invitation to be part of Google+. After a 12-week Beta launch to a limited number of users, search engine giant Google last week opened its new social network to everyone – eliminating the biggest drawback for the site compared to Facebook, which now has some 750 million users around the globe.

So will Google+ now begin building a user base that rivals its much larger competitor? Time will tell. But a few improvements to the site, and simultaneous changes at Facebook, may give Google a slight leg up.

Have you been to the Google search page recently? You’ll notice a big blue arrow in the left hand corner that directs you to where you can join the social network. Already on Google+? You’ll see the arrow, too, if you’re not logged in – a bright reminder to log in and see what’s happening in your circles. (For a quick 101 on the features of Google+, see our blog post about the Beta launch).

In addition, Google has added some new features to entice new and returning users. Google Hangouts, its service for allowing groups of friends to have live video chats, can now be used from a mobile phone if you download the new Google+ app. That is, if you’re using a newer Android device.

Coincidentally, Facebook also made some changes to its format last week – unannounced tweaks that (as often happens with Facebook makes changes) have upset some of its users. Log into your Facebook account now and instead of a feed of the most recent stories posted by your friends, you’ll first see a feed of the top stories since your last visit – with the corner colored blue so you can spot them easily. In addition, a new real-time ticker appears in the upper right corner of the homepage that shows a stream of updates, comments and so on.

Will Facebook’s changes, coupled with some of the unique features of Google+, help prompt some social networkers to give the new online community a try? It’ll be interesting to see, in coming weeks, if Google reports an increase in users.

Are you using Google+? Do you like Facebook’s changes? Tell us what you think.