Regarding spells - not all classes had access to spells and quite a lot of them were unique to a class.
But all the spellcasting classes had spells. And a good number of the them did double up over multiple classes, especially the lower level ones. But very few people ever complained the cleric was less unique just because the druid and bard could also heal. And every single wizard spell was doubled up because the sorcerer's spell list matched it.
At the end of the day... it really comes down to half the people thinking its the crunch that makes classes unique, while the other half think it's the fluff that makes a class unique. Half the people thought the sorcerer was a unique class in 3E because they cast their spells differently than the wizard... while half the people saw barely any differentiation between the two because they shared a spell list and there was barely any fluff on the sorcerer whatsoever.
So what will end up happening is that half the people will see weapon-using classes using expertise dice and say they are now all pretty much the same and there's no reason to play one over another... while the other half will see the distinct separation of the fighting styles that one class gets that another won't, and add that to the story of the class of why, where, and when he does what he does... and find them each unique.
But let's also not forget here... this is just a trial. There's no guarantee that it's a definite that expertise dice will be used for more than one class. There's always a good chance that this change will get rolled back if enough people do not think it works or muddies the waters. So the best thing you can do is playtest several adventures with a fighter and a rogue and really find out if the fighter is now "not worth playing" because the rogue shares ED.
You know what I think the
real Fighter/Rogue issue might end up being, and the one I think many people should playtest? It's the DEX-based Fighter alongside the Rogue.
That might be the one place where both classes having EDice might make the DEX-fighter feel a bit also-ran. Does a dual-wielding Fighter with a Dualist fighting style end up losing ground to the Rogue now that they both power their abilities with EDice? That might be the place where something different might need to be added to the Fighter to make sure it doesn't get overshadowed. Because otherwise we'll end up with a pseudo-4E situation where Fighters end up defaulting to the heavy-armor tanking spec while the Rogue becomes the light armor, weapon finessed swashbuckler spec. Which I don't think is what anyone really wants to see. The Dex-based Fighter should remain a viable option.