Seer : Seer also needs a particular deck to work at its best, but it's very versatile and can work even in non-optimized decks. With seer you may focus a little more on the 2-4 range and sometimes you may want to trash coppers before estates. So this is a nice lab variant and we needed more lab variants. Very good.
Seer is much better than a Lab variant in most decks. It beats lab once 33% of your deck is in the $2-$4 range. Your deck starts 30% $2-4 and drops to 27.3% when you buy the seer. But honestly, it will be over 33% if you do most any of the following: trash the coppers, buy silvers, use a $2-4 action as anything but a singleton. Yeah it doesn't like debt or pots, and a deck full of $5s is bad ... but you should generally expect Seer to draw better than Labs in most decks.
And more importantly you can change the top deck order. This means you be sure to place villages on top (or bottom) as needed which is pretty strong. You also can get massive mileage with other top deck control - dump cards on top with Kc/Count and draw them all back, with deck drawing you can discard and pretend you have Champion/Hgrounds, alternating Seer/Apothecary is insanely good and even Navigator can work. Seer gets even better with silver gainers or $3/4 gainers in general - of which there are many.
Experiment : This is a very interesting lab variant and the tempo is crucial here. If you get experiments early, you will benefit from its natural deck-cycling and you will get $5+ more easily, but at the cost at losing experiments early. If you get experiments later in the game, losing the experiments hurts less and they are pretty much cheap laboratories. So, the most important about experiment seems to be gaining them at the right moment : very interesting decision. Excellent.
Expedition costs exactly the same and gives you the same net effect most of the time. Expedition is not bad. What makes Experiment is that it tends to be so much more flexible: you can choose not to play them when you draw particularly well, you can use Tr with them for engine spawning, you can gain them off most any gainer, and they can function as a pseudo +buy (e.g. Forager nets a +buy every other turn), they accept cost reduction, they are immune to more attacks than Expedition (even the things, like Swindler, that can nuke them typically have low odds), and they can draw cards gained mid-turn. You lose control over exactly when in the shuffle they hit, but in general they seem much stronger than Expedition.
Ultimately, there are a lot of times where Experiment should basically be gained every turn with spare $3 gains/buys.
The really fun thing is how the pile warps the end-game. 5 gains to empty a pile is wonderful for threatening end game. But also fun is the option of cease gaining them to stretch the game out.
Flag bearer : I'm worried that the battle for the flag can turn games into ridiculous slogs, because it seems to me that even if you are getting more flag bearer than your deck can afford, the flag is too powerful to be ignored. The on-trash effect is very useful for that kind of situations. But what if we have no trashers ? Time will say. Anyway flag bearer a nice card that use the artifact mechanic in a very elegant way. Very good.
If the Flag is worth going for, at all, is worth buying one more bearer than the opponent. The more junked your deck, the more valuable that 6th draw card is to get.
As it favors second mover, you often benefit from waiting for your opponent to flinch first & grab it (or conversely grabbing it when you opponent is going to be too tempted by the $5s). I suspect there will eventually be a bunch of high level games where nobody buys it as a single River's Gift isn't worth the worst possible terminal silver. This calculus changes if you realistically expect to empty the pile or can get something useful out trashing the suckers.
I strongly suspect this will be a terrible Bm crapshoot.
Swashbuckler : I'm not sure how often treasure chest is really worth it, to me it's not the most important part of the card. The most important seems to gain the coffers, and this is where the card gets interesting... but also a little bit too random for my taste. Good.
Chest is extremely valuable. The comparable action is a prize that takes up a draw slot and gets you the gold one turn sooner at best. Other gold gainers have some pretty big detriments (Bandit can steal from itself, Mint requires trashing treasures in play, and basically all of them but Courtier are terminal).
That something out your mid-game (when you gain coffers) is really valuable too. Eventually even gold clogs decks, some faster than others, so you can let it go pretty often in the late game.
Treasurer : It seems to me that with treasurer players have two ways to play : either they fight for the key, or they trash coppers. Gaining from the trash is potentially interesting with tfb. Very versatile. But like flag bearer, the artifact seems strong, maybe too much. Good.
Gaining treasure is quite strong, with something like Remodel or Counterfeit you are basically playing Courtier with dual-action type; oh and as a benefit you thin out the early coppers too. I am not sure that key is really all that strong. Sure you can hit price points more easily ... but trashing coppers is also powerful. Ignoring Key is dangerous, but so is not trashing soon enough.
Silos : I like card that makes copper better (rip coppersmith). With silos, you often still prefer to trash your coppers but at least silos almost garantee a good starting hand. This is not the most interesting project to me but I think we needed more ways to play around coppers. Very good.
More importantly, silos makes it very easy to hit power cards sooner. Things like Remodel/Estate get a lot better with Silos; things at $3, like Develop are exceedingly good.
The other nice thing is that it can create a stock of cards in the discard to draw at the end of the deck. Moving copper to the end of your draws means you can tolerate a lot more coppers.
Citadel : The thing I like the most about citadel is the once-per-turn village potential. A recent game showed me that it can be a vast trap, but I think in the right situations it can work very nicely. Otherwise, citadel still seems to be an auto-buy almost always, it bothers me a little. Also there is the randomness about having the best card to throne in your hand. Good.
Citadel loves the Lab family; absent villagers/durations/CotR you either get to Throne a terminal or go for some type village effect. It oddly can also work well with cheap terminal silvers. Once you have it, you can spam the deck with Silvers and Terminal silvers. Getting to $8 is easy as all get out with when you need $4 from 4 cards.
Innocation : I love this new way to play actions during the buy phase and I did so many awesome things in just few games : With estate in hands I bought free barons, with golds in hand I got Governor for the remodel effect, I princed a candlestick maker... This one of the funniest and most creative cards of the new set. Might be too strong but I don't care. Excellent.
Almost complete auto-buy, often with your first $6. Works exceedingly well with anything that gives +buy and most attacks. It functions as a Pseudo-village, besides the obvious gain a non-terminal, you have fun things like buying a clutch terminal for a second action (e.g. Bishop/Monument, Squire/Chouse)