Some of the speakers you are considering (maybe not anymore) appear to have come with a "all-in-one" portable system.
One thing about speakers that came with these systems is they are often designed exclusively for use with the system they are packaged/sold with.
Usually, if you listen to a favorite song on the all-in-one system and then compare the sound to you "real" system, you will readily hear worse sound when the same speakers is used for you real system.
Another test you can do is play your Andrew Jones speakers using the all-in-one system and see if they sound like the same speakers you are familiar with. Some of those systems use neutral electronics and speakers, but others have custom EQ'ed the speakers and electronics so they work pretty good as long as you don't try to integrate them into another system!