The iPhone 5 was outperformed by six other brands, including smartphones from Sony, HTC, Blackberry and Google, according to Which - the UK consumer watchdog.
The HTC One was in second place and Sony's Experia 'sneaked' into third place, ahead of the Google Nexus 4, but the Google device does have the advantage of being up to $300 cheaper than its rivals.
The Daily Mail said the findings will be a blow to those iPhone 5 fans who have wrongly assumed their trendy mobile, the best-selling in the world, is also the best.
The Geekbench speed tests, which benchmark the devices - the higher the score, the faster the phone - saw the Samsung S4 score 3,188 and the iPhone 1,664. The HTC One scored 2798.
The much-acclaimed iPhone 5 was even slower than the Samsung Galaxy Note 2.
Speed is needed for popular tasks such as browsing websites, playing games, editing pictures or using apps.
The Samsung Galaxy S4 was almost twice as fast as the struggling iPhone 5, which is set to be replaced shortly by Apple.
The Samsung S4 has a 1.9GHz quad-core processor, while the Apple i5 has a 1.2GHz dual-core.
The Which organisation said: 'Bigger processors do not always mean better speeds - that's why we put all the handsets through the same test. This measures processor and memory performances across smartphone platforms to provide a standard speed rating.'
1.Samsung Galaxy S4 - 3188 points
2.HTC One - 2798
3.Sony Xperia Z - 2173
4.Google Nexus 4 - 2134
5.Samsung Galaxy Note 2 - 1950
6.BlackBerry Z10 - 1698
7.Apple iPhone 5 16GB - 1664
Which? said: "Undoubtedly, Apple will upgrade its next iPhone with an improved processor when it launches later this autumn. For the moment, Samsung's Galaxy S4 is the phone to beat when it comes to speed."