Well, my knee jerked right on up and voted oil. This is due to a deep seeded love of skipping past Ironclads and upgrading/building packs of Destroyers. Besides, who doesn't love Tanks?
Uranium also allows you to build destroyers, subs, transports, battleships, etc. Tanks are nice, but nukes are nicer. In late game Uranium >> oil.
- Main advantage of the horses seems to be the ability to rush. Rushing sure is a game winning strategy but... what if one doesn't rush but builds wonders instead, or RExes ?
You retain excellent barb defense, a very strong field unit that can keep you alive easily with siege, and the ability to cavalry stomp people. Not a bad deal. However, when you really NEED that rush, having it can turn the game from "extremely difficult" to "easy win" on a dime.
- Horses units die. One's more likely to suffer from war with horses than with metals. With heavy losses, one may also have to invest more hammers than with metals.
Nice try, but it's the other way around. Horse units have withdraws (IE on average they survive more attacks). Many of the horse units ignore first strikes, making them better vs archers. I believe I said this before and am not amused that it's not being considered here, but horse-based rushes fight FEWER units than metal. FEWER. LESS war weariness. Not more. Less. Period. Later on if you involve siege then WW levels out as both armies have to wait for it, but the 2 move potential still gives them the edge.
Chariots need (I suppose) a high production capital. At least 10+ hammers. 15 would be great but is a rare instance.
City tile: 1 hammer
3 hills: minimum 9 hammers (on the vast majority of map scripts, capitols are guaranteed 3 hills).
Horse tile: 3+ hammers.
I'm not seeing the issue here? You're almost guaranteed 10 hammers/turn and are likely to get more at pop 5. By the way, whipping before investing in a granary is inefficient (and it is still inefficient to whip away grassland hills once you have the granary generally, though very high food counts might change that the difference won't be immense that you're taking a big hit by simply hammering out units), and CHARIOT play comes way before you'd bother teching pottery and building a granary. So does an axe rush. If you're trying to do an axe rush ASAP and you stopped to go to pottery and build a granary instead of chopping axes + using comparably efficient mine tiles, you screwed up. Whips are relevant later with a granary obviously, but by then we're out of the true ancient era rush stage.
- One can promote highly his chariots/HAs, it won't increase their durability. Same isn't true for city raider units. CRIII units don't die.
Derp.
I'll address your assertion on this even though it's rather flagrantly false

. A simple combat I axe will have winning odds vs both CR III axes and CR III swords if he's fortified behind walls (85% defensive bonus). It's much easier (and generally faster) to come by walls + combat I than CR III. A CR III unit is also a sitting duck in the field AND it's still slower than mounted, so you STILL have to kill more units = more chances at losses. Not only that, but you have to actually make it to CR III.
CR III sword vs wall city archer with fortify: 6 vs 4.2 + first strike
Combat III HA vs wall city archer with fortify: 7.8 vs 6.75
Of course, it's easier for HA to reach combat III since with stables they start with more XP and need fewer battles to do it.
HA has slightly worse odds to win outright...but still can withdraw too. Of course, it actually fights fewer units again because opponents have fewer turns to whip en route, fewer turns to stack fortification bonuses, and fewer turns to shift forces and concentrate them. But go ahead and keep telling us how the swords don't die while somehow mounted does

.
Comparing CR III axes to chariots is silly. Chariots are a speed rush unit, and when using axes in that role you aren't going to have CR III legit. You might get CR II, but will then have to wait to fully heal before even using THAT. Keep in mind that combat I is often better vs archers in cities than CR I, so you actually take a small dip at 3 xp by going for it in some cases. Higher axe base str is offset by the cheaper cost of chariots and fewer units they face. It's not an easy comparison, but chariots tend to do better for rushes in practice because they catch targets defenseless more consistently.
@ X-Bows : sure, they're no threat to horses ; spears are. And if you have X-bows, you surely have a couple spears. What crossbows do is they stop swords dead and are a very real threat to maces.
My point was that you can't really press HA/cata with anything but very late medieval or noobyphants, and that point is correct. Spear are pathetic vs HA with even a little collateral.
Overall, power vs flexibility (?) is the question. In my eyes. If my stack can use a varied set of units, I'll be happy. Speed has its own merits, I won't deny that. But it also has its costs. Metals offer advantages that horses do not and vice-versa.
While true, your representations have *GROSSLY* under-valued the impact of speed when it comes to units faced, gains, opposition's capability to whip, and concentration of one's own forces.
Most stacks outside of medieval don't need varied forces to be effective. They need collateral damage or a tech lead.