Thank you for starting this tread. This is such a difficult question. I like parts of all sets and dislike parts of most sets. I do not yet own Alchemy, Allies, or the about to be released Plunder.
Dark Ages may be my favorite. The box is packed with so much and has the most cards i like. First there are Shelters nice to twist play. Then there are Ruins, less harmful than Curses. Spoils are kewl. I like all the trash interactions.
My next favorite is Adventures. I love the tokens the most and wished future sets would make some use of them. It was nice to get more Durations. The Reserve cards are nice. This included my first Horizontals, Events, which are kewl since they can add a new dimension to the game.
Renaissance would come in a solid third. This set has so many good cards and some of these also have Artifacts. Artifacts are a nice bonus to struggle against other players to posses. This set gave me my second Horizontals, Projects, which is nice to have some special abilities that others may not have. This set gave me villagers and Coffers. I had not got the Mixed box (Cornucopia + Guilds) yet.
Seaside was my favorite set, until i got the above sets. I got it after the Original, Intrigue, Prosperity, and Hinterlands, which to me all seamed too basic. The idea of Duration was fantastic. I also liked having so many new mats.
Menagerie is a nice set. I have not had it a year yet. Ways are kewl, but don't seams to be used that often. I have included a Way in every game, almost a dozen now, and they are rarely used. I like Horses, but it would be kewl if there was a similar card with a chain longer than one.
I just got Empires, mostly for Landmarks and to try the Debt mechanic. It is nice to use the victory token again, since i largely avoid Prosperity. Split piles seam like an intriguing idea in theory, but not so much in reality. I may need more time with them.
I like Heirlooms from Nocturne, but would like a set without them connected to Boons and Hexes. I'm developing my ouw fan-made set to remedy this.