Organic Groups vs Group - on D7 vs D8?
... Am I correct to understand that Group module does not allow content to exist in more than one group at a time ...


Yes that is correct, but you seem to not take into consideration that the Group module has the notion of Group Types, and when you create "a" Group, you have to specify which its Group type is (compare to creating nodes, which you can only do if you first specify the content type for that node).

Moreover, a user can:


have multiple levels of access (none, read, update) to some group (outsider, member, etc).
be member of multiple Groups.



  ...  and hence based on my requirement OG is the better choice?


That's a matter of preference (opinion based), e.g. if you prefer to go for D8, at this time, IMO, the Group module is way more stable ...


  
  Should I assume that OG 8.x-1.0-alpha2 is not stable enough to use for a production site, and that I should stick with OG 7.x-2.10 on Drupal7 for now, and wait on the benefits of Drupal8 until OG matures at least to RC1? 
  


If you do decide to go for OG, then for the sake of stability, at this time, D7 seems to be the way to go.

Read more: What are the features of the Group module versus Organic Group module?