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As far as I can see, if the content is exactly the same on both the .com and .co.uk sites and you intend to keep it this way for the forseeable future, then there is no point maintaining both. Put all your efforts into developing and maintaining the .com site. Not only will this ensure that you are able to build the authority of one domain, it will also ensure that all your social media activities will be for the one site rather than sharing both .com and .co.uk URLs. Alternatively, if you want to differentiate your content slightly for a global and a separate UK audience then hreflang across the.com and .co.uk sites is the way to go.

Ok, too bad. But thanks for the reply

According to my experience, it also doesn't add the likes from bitly or other URL shorteners.

To date my site does not get a lot of user engagement via G+, but I am helping those who write for our site with their G+ accounts.  Our writers are experts and practitioners in our niche and they are not (nor do I expect them to be) SEO experts.  I explain to them the potential benefits of G+ and help them set up rel=author to get credit for both the articles they write for our site and also the articles they write for other sites.  I also encourage them to increase their circle.  I'm confident our readers would prefer to read articles by experts in our field rather than ghost written articles.  I also compensate them better than ghost writers.  I think it's a win/win if these experts' photos are in the SERP and they get the recognition they deserve and it should improve the CTR as well.

Both Google + Bing should be fairly accurate coming directly from the actual companies data. So..., are Bing users typical kind of users who uses other search phrases? Could very well be true. The fact that there in this case and for most people as well about 10x more search volume is definitely part of the issue. Hope this helps

Thanks Reload Media and Deb Dulal Dey. The job is done (for a while now) and the results are even better than hoped for. In the beginning, there was a little (very little) drop, but within two weeks they climed up. Now we have doubled the organic visitors! So, it turned out great

Before you make a big move like this with a money site you need to know what you are doing.  There are many ways that website moves can go wrong because the person doing the move lacks knowledge. When a website is moved your goal should be to have a huge increase in sales.....  you are worried about being hit with a huge loss.  That tells me that you should hire an expert to assist you and teach you how this is done. Websites should be moved by a person who has the knowledge and care to do it properly.