Same speed, but... They can move onto hills, forests, and cross rivers after moving, and still start their work that turn. So actually they do save quite alot of time; This is especially noticible, and powerful when using the ever important choprush.
I'm a fan of the fast worker, It's solid. but I don't think they are great like some of the stronger UUs.
I agree with most except the last line(FW worth >> stronger UU- fast worker lets you have more tech. advanced UU, which negates most beatstick UUs). If fast-workers build improvements 1.5x faster, it would be an unbeatable advantage, for you'd essentially be researching tanks by the time others are researching riflemen given how fast your cities would be built up.
They get to the tiles muc faster, especially when empires are getting bigger- i've seen fast worker cover same ground in 2-3 turns on road when vanilla workers would take 4-5 turns. Plus as Phungus said, start work on same turn after crossing river/into jungle.
Essentially speaking, you are looking at your mine being built 2 turns early/plantation getting done 2-3 turns earlier, etc. on average, depending on the whole logistics ( eg, how far is your worker when calendar is available and city with plantation crops that need to be built up?).
So essentially speaking, finishing a farm/pasture 1 turn earlier or building mines/plantations 1-3 turns earlier might not seem much but consider how much building your worker is doing over the whole game- it is a HUGE advantage to have. You are building 50-60 farms, 50-60 mines, 10-15 plantations etc per game on average and on each one the FW is finishing 1-3 turns earlier because of movement logistics. That adds up insanely near the end-game.
Plus you are forgetting- with your movement bonus, fast workers will build roads & railway at near-warp speed compared to vanilla workers since they take 1 less turn to build every tile of road due to their movement bonus(think how much quicker he is going to link a major city of yours to a minor one needing a road connection to capital).
And if you think about it, having a fast worker is almost equal to having the expansive trait added to your trait in mid-game. If you tihnk about it, expansive trait provides you with faster granary & harbour- things that help your food situation. But cities get better food if they are connected to the 'culture network' faster- your 'warp speed road-building worker' will essentially make your town grow faster because it establishes connection with your capital MUCH faster (thus impacting on happiness & growth factor much quicker).
If you play as India and you plop a city down on decent ground ( ie, not on the polar cap/middle of desert and the city has potential to grow) and the next nearby foreign civ town is on equally good/better agricultural grounds and has a population of 2-3 already, your Indian city will still outgrow the foreign city by the time population hits 8-9.
If you know how to use the fast worker skill efficiently, India is an incredibly powerful side to play with. IMO, fast worker UU is much more subtle in its impact but far bigger than any other UU militarily speaking (though a good player on rome can own a good player of India playing p2p if they spawn close by) because it has synergy effect with its leadership traits.
Remember, both of India's leaders have spiritual trait, so there is no anarchy.
Over the course of the game, if you switch civics 3-4 times and experience 2-5 turns of anarchy(depending on diff. setting i guess), it is essentially equivalent of having 6-10 workers getting 6-20 free turns through the course of the game- that is essentially equivalent of me having an entire 20 population city being built over my next best rival in 100-120 turns!
If you think of 'most powerful unit' as not one having the best 'whacking potential' but as the one which benifits your empire & your civilization's survivability/development the most, the FW is quite easily the best.
Since India doesn't have aggressive traits or a good unique beat-stick, India's big challenge is essentially staying alive and up to tech.power with the rest by the time it has 7-8 cities well set up(with say 4-5 population minimum in 7-8 cities).
If India makes it to that point, you shouldn't lose.
no joke, think about it.
to (unlikely even because he'll probably survive) kill one unit and then you have to have more chariots to beat the axemen after that. Since you'll pretty much always have a large numerical advantage when attacking (I'd say at least a 3:1 ratio at the border) that one additional spearman won't exactly cost much production-wise or else.
with the Phalanx, I think everything's been said.
(I don't have any supporting evidence though.)
