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Are cellphone users finally souring on Apple? Looks that way.

The American Customer Satisfaction Index (ACSI) is out with a new brand study that ranks 10 popular smartphones. Three versions of the iPhone were included in the survey, and none could crack the top two.

Samsung’s Galaxy S4 was launched right after ACSI completed its survey, but the S3, which was several months old at the time, came in at the top of the heap with a score of 84 (on a 100-point scale). Not to be outdone was another Samsung Galaxy device the big-screen Note II which also scored an 84.

Those phones were followed by a trio of iPhones the 5, the 4S and the 4 which scored 82, 82 and 81, respectively. That’s not bad considering that the iPhone 4 was released way back in 2010. The Motorola Droid Razr Maxx HD, the Samsung Galaxy S II and the Motorola Droid Razr all posted respectable scores: 80, 78 and 77, respectively.

Not only does Samsung edge ahead of all iPhones, Apple customers themselves dont see much difference between the iPhone 4, 4S or 5,” says ACSI Director David VanAmburg. 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 Apples dominance in overall customer satisfaction.”

Then there are the BlackBerry phones. The Curve only garnered 67 points and the Bold got 64 yet another sign that BlackBerry, once a behemoth in the industry, is in serious trouble.

The survey counters many previous studies, including a J.D. Power report from March, that said the iPhone was far and away the leader in customer satisfaction. Some industry insiders have question Apple’s ability to innovate in recent months, especially considering the fact that its competitors are coming out with multiple phones every year.

Interestingly, the ACSI survey revealed that consumers in Korea Samsung’s backyard prefer Apple. The National Customer Satisfaction Index (NCSI) in South Korea, which uses the same technology as the ACSI, shows the iPhone 5 has higher customer satisfaction than Galaxy S III.

ACSI data suggest that smartphone users are much more satisfied than are feature-phone users, which should come as little surprise. Overall, smartphones earn a customer satisfaction score of 76 compared to 69 for feature phones, which ACSI says is another strike against BlackBerry.

Like Apple, BlackBerry offers smart devices only, yet the company stays firmly entrenched at the bottom of the industry in customer satisfaction,” said Claes Fornell, ACSI founder and chairman. This does not bode well for BlackBerry considering that smart typically outperforms feature when it comes to cell phones.”

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