Should I start with the officially released last version (1.05?) or dive right into the deep end of the pool with the New Horizons mod?
If you want to play one map just to see if the game suits you or not, go vanilla.
If you start a campaign, go straight for New Horizons. The campaign in Eador is crazy long, so it's very unlikely you'll complete vanilla one and still have the mental strength of doing another playthrough with NH.
What you need to know before making decision about Vanilla vs NH:
1. The balance in vanilla game is broken. It won't take you too long to figure out the most game-breaking spells, of which the most ridiculously broken one is
and then just stick to one strategy during the rest of the campaign. Same goes for units. NH will keep you engaged and force you to practice different approaches depending on current map, opponents, situation.
2. Vanilla AI just doesn't work, period. Again, once you figure out the holes in balance, the game will stop being challenging. At all.
3. NH has a single downside and that is aesthetics. It adds a lot of content and some of it might feel misplaced. Witchers are probably the most notable of such additions. The fact that witcher's sprites look just like Geralt doesn't help things either (the NH devs on the official Rus forums stated they plan to change the sprite sometime in the future, though).
NH adds some cool stuff but it also raises complexity a lot (do we really need tier 1 units with 2 rows of abilities?)
It's a complex game to begin with. If you don't like complexity, why even play Eador Genesis?
Also NH makes the AI cheat a lot more blatantly and efficiently than in the base game, and the base game is not easy already.
No. It was stated over and over again by NH devs that the mod was developed
with a single difficulty setting in mind. Once set your difficulty higher, you get hordes of AI opponents assaulting your provinces in the first week. Either you played on higher difficulty levels, or you are just bad at the game.
What do you mean by "cheating"? NH's AI has state-of-the-art algorithm. If you don't have ranged units and attack a group that has some, that group will not advance their melee fighters and shoot you from a distance until you get too close. Just one of most simple examples. In general, during tactical combat AI does not make mistakes and punishes your own mercilessly.
Strategic AI, while not genius, is still better than vanilla one. I've completed both vanilla and NH campaigns. First one was a slog. The latter was extremely fun and thought-evoking.