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A new smartphone brand study could be the harbinger of a new world order. Two smartphones made by Samsung Electronics were the top U.S. scorers, ahead of various iPhone models from Apple Inc. (NASDAQ: AAPL). In an interesting twist, Korean customers still prefer Apple’s phones.

The survey, conducted by the American Customer Satisfaction Index (ASCI), reported that the Galaxy S III and the Galaxy Note II from Samsung were the top-scoring phones, followed by three iPhone models: the 5, 4S and 4. In general, smartphones get strong marks for feature variety, design and ease of use, while battery life continues to be an issue with users.

An ASCI executive noted:

The latest earnings report from Apple was better than expected, but the name of the game for Apple has always been innovation. Samsung, on the other hand, shows a strong upward ACSI trend from the Galaxy S II to the Galaxy S III. If the S4 performs as well—or even better—in the eyes of customers, Samsung could threaten Apple’s dominance in overall customer satisfaction.

Here’s the ASCI ranking, from the least to the most highly rated smartphone. The prices listed are not the lowest, the highest or an average. There are simply too many sellers to make that possible. Think of them as suggestive. Market share data is extrapolated from total market share by manufacturer where available.

10. BlackBerry Bold
> ASCI score: 64
> Market share: less than 1% (2Q2013)
> Price with contract: $100 (Verizon Wireless)
> Price unlocked for Model 9930: $650 (Best Buy)
> Manufacturer: BlackBerry Ltd. (NASDAQ: BBRY)

The Bold brand of QWERTY keyboard phones from BlackBerry was first launched in 2008, and the latest models were released in 2011. More than anything else, the Bold’s age works against it. It is not upgradable to the new BlackBerry 10 operating system, although the family line includes both keyboard and touchscreen models.

9. BlackBerry Curve
> ASCI score: 67
> Market share: less than 1% (2Q2013)
> Price with contract for model 9315: $50 (T-Mobile)
> Price unlocked for Model 9360: $300 (Best Buy)
> Manufacturer: BlackBerry Ltd.

Another venerable name from BlackBerry, the Curve was first launched in 2009. The company introduced the 9315 in January of this year, just one week before launching the Z10 touchscreen phone. Not the brightest marketing move ever, but then, the keyboard Curve doesn’t really compete with the new touchscreen phone.

8. Droid Razr
> ASCI score: 77
> Market share: N/A
> Price with contract: $300 (findthebest.com)
> Price unlocked: $650 (findthebest.com)
> Manufacturer: Google Inc. (NASDAQ: GOOG)

The original Razr brand phone from Motorola was introduced in 2003, but the touchscreen version was not launched until 2011, with the Droid moniker attached to it. The Droid name is specific to the Verizon Wireless version of the phone. At the time of its release, the Razr was the thinnest 4G smartphone on the market, according to Motorola.

7. Galaxy S II
> ASCI score: 78
> Market share: N/A
> Price with contract: Free (T-Mobile)
> Price unlocked: $264 (Amazon.com)
> Manufacturer: Samsung Electronics

The Galaxy S II (or S2) was launched into the market in early 2011 and reached 10 million in worldwide unit sales just five months later. The phone also helped cement the Android operating system into its current position as the leading operating system in the smartphone sector. The S II was cited as the best Android phone yet available at the time of its release.

6. Droid Razr Maxx HD
> ASCI score: 80
> Market share: N/A
> Price with contract: $150 (Verizon Wireless)
> Price unlocked: $750 (Best Buy)
> Manufacturer: Google Inc.

The Razr Maxx HD was launched in October 2012 exclusively with Verizon Wireless, using the Droid moniker the carrier licensed from Lucas Films. The device competes against the top-of-the-line phones from Samsung, the Galaxy S4, and Apple, the iPhone 5. The HD features a longer-life battery and a Gorilla Glass cover, both of which led at least one reviewer to say shortly after the launch that it was among the best Android phones available.

5. iPhone 4
> ASCI score: 81
> Market share: 5.4% (2Q2013)
> Price with contract: $100 (Verizon Wireless)
> Price unlocked: $450 (Apple Store)
> Manufacturer: Apple Inc.

The iPhone 4 was released in June 2010, and pre-orders for the phone sold out within 24 hours. Some 1.7 million of the phones were sold in the first three days of its availability. Some phones had an antenna problem that Apple was a bit slow to fix, but that really did not hurt the popularity of the device that much. At the time of its launch, the iPhone 4 generally was considered one of the best smartphones on the market.

4. iPhone 4S
> ASCI score: 82
> Market share: 9% (2Q2013)
> Price with contract: $100 (AT&T)
> Price unlocked: $549 (Apple Store)
> Manufacturer: Apple Inc.

The successor to the iPhone 4 was launched in October 2011, and 4 million units were sold in the first three days of availability. The phone was virtually identical in appearance to the iPhone 4, and internal differences were also slight. The voice-activated Siri software was the major operating system addition on the 4S.

3. iPhone 5
> ASCI score: 82
> Market share: 15% (2Q2013)
> Price with contract: $199 (AT&T)
> Price unlocked: $649 (Apple Store)
> Manufacturer: Apple Inc.

The iPhone 5 was launched in September 2012, and Apple got more than 2 million pre-orders for the device. Apple sold 5 million units in the first 3 three days the iPhone 5 was available. In addition to the market battle, the latest version of the iPhone really heated up the patent wars between Apple and Samsung. The high-resolution screen and the larger screen size were the main changes to the device’s hardware.

2. Galaxy Note II
> ASCI score: 84
> Market share: N/A
> Price with contract: $300 (AT&T)
> Price unlocked: $650 (Best Buy)
> Manufacturer: Samsung Electronics

The Note II was released in October 2012 and sold more than 5 million units in its first two months on the market. The major innovation here (if one can call it that) was the pressure-sensitive pen that allows a user to preview content by hovering over it.

1. Galaxy S III
> ASCI score: 84
> Market share: 7.1% (4Q2012)
> Price with contract: $100 (Sprint)
> Price unlocked: $600 (Best Buy)
> Manufacturer: Samsung Electronics

The Galaxy S III was launched in May 2012 and was the most successful smartphone Samsung ever kicked out the door. There were 9 million pre-orders worldwide, and the company shipped 20 million units in the first 100 days of availability. The phone was widely praised at its introduction for its voice application, processing speed and screen display. As a precursor to the Galaxy S4, the S III set the stage for a big boost for the new phone that launched in April of this year, too late to be included in the ASCI survey.