I only own second edition, but I'm familiar with the removed cards from watching Dominion videos. This means I can't really answer the question as stated, but I can answer a related question: "which cards, if any, are you sad about not getting to play with?"
My generic answer is "any card with a unique ability".
Messenger,
Nomad Camp and
Scavenger replace
Woodcutter and
Chancellor just fine; I don't miss any of those.
Scrying Pool has the
Spy attack.
Adventurer, meh, usually
Smithy does the same job better.
I've used
Feast and
Thief in puzzles, but they're fully available in that context. I don't think I'm missing out on anything but not being able to play them in real games.
Bandit is a fine replacement for Thief, and while Feast isn't exactly replaced by
Artisan or
Altar because you can't open with them, I still don't really feel like I'm missing out.
Mill replaces
Great Hall perfectly and
Patrol replaces
Scout except as the butt of jokes—and in that context, Scout is a favorite of
mint.
I think
Secret Chamber has something unique—a reaction that interacts interestingly with top-of-deck attacks, e.g. Thief,
Swindler, Knights, even
Ghost Ship. But the on-play ability is sufficiently weak that you rarely go for it, so the thing that's lost wasn't very much there to begin with. And the effect, meh, okay, it's no huge deal. I don't think I'll miss it.
Next up on the scale of interest level is
Tribute. It does something unique, though the thing it does is sufficiently unreliable that I would hesitate to build my deck around it. As the only village in an engine mirror, it has the interesting characteristic that my greening makes your deck less reliable. Eh, you know, I think it's more fun playing an engine with a reliable village. It had something unique, but of low value.
Penultimately there is
Saboteur. "Swingy and often not great" sums up my impression quite well, but on some boards it can decide the game. Something of moderate value might be lost here. I'm very much open the possibility that I would think something else if I had actually played with it.
Lastly,
Coppersmith. I think it only plays in engines, and I would typically rather trash my Copper and buy Gold than make my Copper worth more. But if you can't trash your Copper yet you can still build a viable engine, Coppersmith is a terminal +$7. That's more than Platinum, for $4. And it can be
throned. That's pretty cool.
So out of the 12 removed cards, I think I'm missing out on two of them, and the value of those two cards is highly contextual and kingdom-sensitive, and I'm not going to buy 1E just for those two cards and the smaller font and the 'he' over 'they', and I'm not going to buy both 1E and 2E, so... I'm happy with my decision, even though it's only
almost strictly better.