The difference is in the history.
History recorded the Ent-C was lost at the Battle of Narendra III
History recorded the Bozeman was simply lost presumed destroyed
Not exactly. Think of it like this:
Timeline 1: TNG's "normal" timeline where Ent-C fought the Romulans and helped convince the Klingons that the Feds are their friends.
Timeline 2: The post-Narendra-III "Fed-Klingon War" timeline where the Ent-C disappeared and was simply lost, presumed destroyed and the Klingons went to war.
We're shown both timelines.
"Cause and Effect"
Timeline 3: This is Bozeman's timeline up till they were caught in a loop. We have no idea what this would look like if they went back to it, hence my joke about the Bozeman could've been part of something to cause a radical change in TNG's "normal" timeline.
Timeline 4: TNG's "normal" timeline that we've been watching on TV since in this timeline, the Bozeman disappeared and was lost, presumed destroyed.
We're only shown one timeline.
Both ships ended up forward in time but the difference is that in "Cause and Effect" we're not shown what the timeline would look like if they were sent back (or not lost). There are multiple histories going on, or as "Parallels" shows us, many variations to history. It's likely that in one of those quantum universes that the Bozeman went back. Hopefully it wasn't to the one with Crazy Riker