They all share the tried and true Beretta action. Fit and finish are the most noticeable differences but there are some others.
Beretta can take a somewhat casual approach to features on their guns. Just because the catalogue says something it doesn't mean the gun will always have those features. So everything that follows are generalizations.
The Silver Pigeon and White Onyx are field guns and are generally (but not always) lighter with narrower ribs. The Beretta field guns sometime come with an automatic safety which means the safety goes on when the gun is opened. This isn't a bad feature in the field but is one serious pain in the ass when shooting clays. If you choose either one of these models check for an auto safety.
The Beretta 686 Sporting is more of a competition configuration. It will have a wider rib, tapered as I recall, may be a bit heavier but will not come with an auto safety.
All of the guns will have choke tubes. Which choke tubes they have depends on the model. Probably Mobile or Optima but Beretta has some other choke tube options as well. All of them work just fine.
They are all 3" chambers except there is a Silver Pigeon S with a 3-1/2" chamber so you could use the Beretta as a back up to your 870 for waterfowl.
The best thing to do is go to a large store where they have each model in stock. Put them to your shoulder, look them over and buy the one that fits and feels best. Regardless which gun you choose it will be a good one.
