I thought it would be interesting to look at the top six competitors (ignoring Catherine). It's a shame Curtin went prematurely and Catherine went from overhated to impossible to get rid of but I'm pretty happy with the top 6 selection.
Alexander:
- Gives access to an amazing unique unit on par with eagles warriors and war carts
- Unique unit further boosts great general points in the classical era, giving you a GG advantage throughout the early-mid game.
- Complete negation of war weariness lets you war almost nonstop. This may seem insignificant if you don't want to speedrun but remember: wars generally become harder later in the game. This ability lets you pick off opponents before they get walls, uniques, nukes and more.
- Healing from wonders is nice but unreliable and helps support near constant war, especially because the last city you want to capture before a war is unnecessary is usually the enemy capital which happens to almost always have a wonderful on deity.
- Weaknesses: Lack of boosts to directly impact battles, domination/religion victory only.
Overall, a strong ability but I wouldn't call it top 3 due to a very noticeable lack of battle advantages excluding the UU which is IMO the star of this boost.
Montezuma:
- Amenities are nice and cool from a flavour PoV. Acts as an Alex lite (see above).
- Star of the show: the attack boost. Attack bonuses are exponential (consult Zigzagzigal's steam guide for stats) but the numbers get ridiculous. Get enough luxuries and you pretty much win.
- Weaknesses: Only really helps for domination/religion victory. Map size is a factor. Needs builders and expansion to be utilised.
Overall, the boost is massive making this easily top 3 material IMO.
Qin:
- Honestly, people are getting hung up on the extra builder charge and its really nice, yes, but in a game where early rushes are optimal a good amount of my early game builders are captured and thus unavailable. Loses lustre later on when this boost can be replicated. Yes, they stack, but other methods have moderate to small opportunity costs and stacking becomes fairly redundant unless you want your spare builders wasting charges/taking 20 turns to get to where they want to be because they were built 50 turns ago across the map.
- The wonder production from builders is nice but I can't help but think sacrificing an early rush for it often isn't worth it. What wonders are even that useful from those eras that you can't often get (Temple) anyway, even on deity. Pyramids? You do need a desert though... Verdict: situationally useful but fairly fun, YMMV.
- Weaknesses: Lack of significant bonuses mid-late game, especially if builders aren't proving too necessary or you would get builders charges from governors and/or policies with little opportunity cost.
Overall, bonuses are distinct and decent but I don't see this on my top 3.
Shaka:
- Early corps and armies make games. The attack bonus is huge (second only to Monty) and the increased production is mitigated by synergy with the impi.
- First half of the bonus is incredibly powerful early-mid game but late game obsoletes.
- +5 combat boost to an early corps/army is a ridiculous boost over even deity AI. Prepare for battles to be won in your sleep.
- Weaknesses: Requires excess production and obsoletes somewhat late game.
Overall, this makes games get won. Attack boosts are massive and come as early as the medieval era, before Monty can compare. Easily top 3 material.
Tomyris:
- +5 strength is +5 strength and that's a large advantage over even deity AI. Enough said.
- The heal on kill is really cool in that it lets your army regenerate in a way nobody else's can.
- Both bonuses synergise well with the light cavalry emphasis of the Civ, letting your horses chance down and eliminate wonder targets for easy health.
- Weaknesses: Again, combat only and full health enemies can be an issue.
Overall, this is a reliable and powerful combat bonus and I'd argue it's worth on any top 3.
Trajan:
- Assumed ancient era start.
- Monument is a nice boost but it's also the only boost. However, it's a very strong and very easy to achieve passive culture boost which makes early game civics like political philosophy (ogliarchy for legions) much quicker to get.
- Monuments are 80 production which is 5-15 turns in most new cities. Again, nice, but is it really necessary? It could be chopped instead.
- Saves time letting you make more useful things.
- Captured cities generally have a monument anyway.
- Weaknesses: Referenced above. Also obsoletes late game when monuments become ridiculously cheap and their boost less important. Favours peaceful expansion over warmongering.
Overall, I'd argue this doesn't really effect the game as much as people think. Good, but barely not on my top 3.
Alexander - To The World's End [9]
Montezuma - Gifts for the Tlatoani [29]
Qin Shi Huang - The First Emperor [30-3=27] My time to make enemies. People are saying others are bad for only contributing to domination/religious victory. This ability only contributes to culture and maybe the builder charge for science and even then it's not game changing.
Shaka - Amabutho [11+1=12] Yes, it's for one victory type but it also makes that victory type trivial.
Tomyris - Killer of Cyrus [34]
Trajan - Trajan's Column [33]