Can any one enlighten me on this one?

The only one I know is that one can check in at a Facebook place. (Not an advantage if you go to your clients location rather than doing business out of your office.)

@amyhallbiz @danielmckean I think there are really only two types – but maybe you can qualify a local business as a page without a place attached to make it sort of 3.  
1.  Facebook Place.  So there is a Place by itself that is created when someone tries to Check in.  Anyone can create a place on their phone (which makes for many duplicates because of misspellings!)  Facebook is trying to consolidate these.  Here is an example of a Place by itself: http://www.facebook.com/pages/Rock-Bottom-Brewery/201044276623351?nr=149635731722531  Usually these have that teardrop thing as the photo and aren’t controlled by the restaurant (although you can “claim” a place to have more control).  So when people check in the restaurant doesn’t get “credit” for the check in if they have created their own Place/Page.  
2.  Facebook Place/Page.  Pages came along and Places were for a long time separate from the Pages.  But Facebook realized that businesses wanted to have more control and have a Place and a Page that were one.  So you can merge them if you have control over Place and Page together.  Now Facebook kind of “automatically” creates a Place for you when you specify your category as a Local Business and add your address.  Now when people are near your address they can check in on their phones and it will update the checkins count on your Page.  Here is an example of a Place that is combined with a Page:  http://www.facebook.com/pages/Rock-Bottom-Brewery-Chicago/216119688949  Notice how they have just under 2000 likes but over 20,000 people have checked in.  It looks just like a Page but has a few advantages.

Place/Page advantage:1.  People can check in2.  You can run check-in deals3.  People can find you easier on their phones when they are looking for places on Facebook and are in your area.

I think those are all the advantages.  If I think of more, I’ll let you know!Hope that clears it up but if you have other questions, let me know!

@andrea-vahl   @amyhallbiz Andrea (and Amy), I wanted to share to further clarify my understanding and original feedback. I rechecked last night how a Page can be set up and I did reconfirm there are different categories an admin can select when setting up the Page. Essentially there are 10 categories with one additional ‘other’ category an admin must select when initially setting up their Page.

One use of categories is to define the type of organization or profile for the Page which Facebook uses within its search algorithms for community members. And Local Businesses & Places certainly allow check-ins. As for the other categories, it still remains unclear as to the benefit other than information loading (informational fields offered)  in the Page About section.

Categories do include Local Businesses & Places, Brands & Products, Companies & Organizations, Movies, Music, Television, People, Sports, Books & Magazines, Websites & Blogs and the catch all “Other” category.
If either one of you know additional benefits for considering a Page’s category, please let me know – or if you can share a link with me to research this topic further, it would appreciated. FB Help is not always helpful and my online  searches last night didn’t really clarify or explain this minor nuance.
Thanks all.

One difference would be recommendations.

Places have a map app automatically added and fans can write recommendations for that place.

As far as I could see it is not possible to recommend a page which is not linked to a specific location. Correct me if I’m wrong…