(Image credits to its owner)
\
I am writing this as a commuter point of view using UberX.
Why I think UberX will a brilliant idea and will be successful in Singapore and will be the next big thing in transportation
Matching demand & supply
It's a on demand service, just like video-on-demand (VOD) on cable TV. For VOD, you watch the show at a time convenient to you, anytime of the day, even at 3am. You don't have to adjust your schedule to match the timing of the show.
Similarly, for UberX, you can get a cab when you want it. You don't have to wait and see if there is any cab roaming around your area. All bookings are done by the UberX app, all are matching the supply to the demand. Gone are the time when you wait for half an hour and you just couldn't get a cab on the road or through the hotline. Great for business meeting where you need to be on time, all the time!
Even if you are in a situation where demand hugely exceeds supply, for example, after a concert / football match, after partying at a pub, Uber have a surge pricing ('X' amount of the normal price). This encourages drivers to come to your area to pick passengers up and if you are willing to pay, you will likely be able to get a car out of the situation.
Taxi drivers
UberX will probably be less successful if taxi drivers are not included in their business. But they are. Instead of competing directly with taxi drivers on the road (difference between taxi drivers and Uber X drivers being you can flag down a taxi along the road but you cannot flag down a UberX), they included taxi drivers in their equation and this increases their number of drivers / vehicles on the road thus better enabling them to match demand and supply.
With taxi drivers their partner, their real competition they have is really with taxi companies and and will force taxi companies to think of other ways to match the competition if their drivers jump ship to Uber. I will talk about this more on UberX (Drivers)
Cashless cardless payment
One of the limitation of not taking a cab is usually you do not have enough cash in your wallet. Sure, more cabs companies are accepting cards but not all companies does. When commuters are able to swipe with their cards, they will likely be more willing to take cabs (spend now think later mentality). Therefore Uber address this problem beautifully by having the payment on the backend and you basically get up and down the car without even thinking about money or your wallet.
For drivers, they avoid fare evasion commutes which I will talk more about on UberX (Drivers)
Private cars
What UberX called 'Scale down limo service'. While personally I am ok with taking taxi or car as long as it get me there to my destination, there are some people who needs to be disassociated with taxis. For example, getting off a BMW 520i (UberExec) is so much better than getting off a Mercedes E220d (taxi) especially when you are meeting your potential client at the entrance of his building.
Of course UberX has the same effect as long as you don't mind your car to be a Toyota or a Nissan instead of a BMW or a Merc.
Past and Present
In the past where there aren't so many people in the country, taxis are sufficient and there is never almost never a long wait for a taxi. If you can't get a taxi on the road, call one and likely a taxi will come in 10 mins or less. However now, when you try to call any taxi company hotline, there is a chance that they tell you: "Sorry, no taxi around your area. Please call again later" That's like usually 10 mins of your time on the phone.
Go to a taxi stand and you will see queues at even off peak timing of the day (3-4pm)
Also the weather in Singapore are getting crazier too with hotter days (just why you think now all buses are air-conditioned) and more people are switching to taxis because they cannot stand the heat. Put it this way, more people are willing to pay a premium to get out of an uncomfortable situation.
Government
The government initiative is for people not to own car but take public transport or shared transport, so I think the government should encourage not only public buses, trains but also companies like Uber and car sharing companies. While they provide private vehicles services, its a more efficient use of these vehicles.
In conclusion, let's put it this way, more people are willing to pay a premium to get out of an uncomfortable situation, be it overcrowding or hot weather or sick of waiting for a prolong period of time.
And for a few dollars extra (for no peak pricing) or even for a few dollars less (for surcharge places with peak pricing), UberX being very likely to have a car pick you up within mins, it's really a no brainer which to choose, especially if time is precious for you.
Rates
As at 15 Jul 2015, UberX charges $3.50 base fare + $0.25 per min + $0.50 per km.
Rates are flat and there are no peak period pricing / additional surcharge.
Taxi pricing are
$3.50 (average) base fare (1st KM) 3.50
1 to 10km every 400m - $0.22 4.95
10km and above every 350m - $0.22 6.30
Every 45 sec waiting time - $0.22
Surcharges apply when applicable.