A minor annoyance in Dominion is remembering how many actions you have left to play. Several cards give you additional actions, and then of course those cards require an action to play, so the math gets... yeach. It's not gamebreaking or anything, but it means a lot of counting on your fingers, which can be detrimental to managing a hand of cards (and Marduk help you if you lose count and have to retrace your steps).
Heart of Crown neatly solves this by simply putting an arrow on the right edge of cards that don't require an action, and a second arrow on the bottom edge of cards that grant an additional action, and require that each card (after the first) must be played with a arrow pointing to it. It's extremely intuitive, involves no counting, and also makes it easy for opponents to check your "math," and it allows the designers to easily balance the various card powers by simply giving them different numbers of arrows without requiring reams of extra text and rules exceptions for what does and doesn't require an action to play. (The arrow icon could be slightly clearer though, it blends in a bit until you know what you're looking for.)
Dominion utilized a clever system of adding purchased "Victory Point" cards to your deck, creating a catch-up dynamic wherein the players with the most points by necessity also have the most cludged-up decks, and forcing the players to make tough choices between improving their deck's functionality or actually gaining points. The problem is that the actual experience of drawing a hand full of useless 6-VP province cards is dull at best and incredibly frustrating at worst.
Heart of Crown expands on this dynamic to create difficult in-the-moment tactical choices. If you draw a hand with points cards, you can "bank" these cards and get them out of your deck (and in fact only banked cards add to your score), but you can't purchase any cards that turn. So a hand full of points cards, rather than a wasted turn, feels like an efficient opportunity to bank, and a hand with some useful cards and some points cards suddenly offers an agonizing choice rather than merely an inefficient turn. Furthermore, this mechanic allows you to better slim and hone your deck, reducing late-game randomness.
In Dominion, you can buy two cards that you intend to play off each other, and then proceed to never ever draw them both in the same hand.
In Heart of Crown, you can stow action cards for use on later turns (depending on how awesome your "kingdom" is).
In Dominion, all the purchasable cards are available right at the start of the game. This reduces randomness and allows for lots of long-term planning, but it also makes the turn-to-turn decisions less interesting since you mostly know what will be available and don't really need to react on the fly. An experienced Dominion player can look at any card setup and immediately say "oh those three cards are going to combo well," and then proceed to pursue that theory and potentially make few to no further choices throughout the game (aside from paying attention to how fast other players are accelerating the endgame). Also having to try and internalize what every action card does right from turn-1 can be a bit daunting if you're at all inexperienced.
Subsequent deck building games like Ascension and Marvel Legendary address this by having a limited selection of random cards to select from. This forces on-the-fly strategizing, but it also increases the random factor, and potentially limits the overall strategizing that a player can do. Heart of Crown finds an interesting middle ground wherein there are always eight different types of action cards available, but which cards and how many of each card shift over time, emphasizing both short and long-term planning (and also reducing setup time). I'm slightly concerned that, because you see a bigger portion of the action cards every game, certain combos might become known and always exploited when possible, but there are expansions to remedy that.
Dominion did not feature adorable anime handmaiden cards.
Heart of Crown addresses this by featuring adorable anime handmaiden cards.
In summary, Heart of Crown is basically Dominion 2.0, and I mean this in the best way possible. Dominion itself is a brilliant, important and innovative game, and Heart of Crown brings a whole host of improvements to the table (and I didn't even get into the fascinating game of chicken involving the Princess powers). There's enough diversity in this genre to justify owning a few different deck building games; Legendary Encounters is a pretty different game from A Few Acres of Snow, for example. But to be honest, given the choice between Dominion and Heart of Crown, I would pick Heart of Crown every time.
...sadly Heart of Crown is not available in English, and as far as I know there are no specific plans to remedy that, which renders this review ...entirely pointless! On the other hand, it gave me the opportunity to type the phrase "please stop the mystic power generator."