Many articles on IT websites claim that Swype is faster than typing on smartphones (zdnet, ghacks, etc). Wikipedia relates the following claim : "The creators of Swype predict that users will achieve over 50 words per minute.". I know that Swype was used to set a new record for fastest typing, but I wonder whether Swype is faster than typing for the average smartphone user (i.e. who did not train to set a typing record).
There is lots of academic research on what is called shape writing or vector typing that is relevant to your question.
"Shape Writing on Tablets: Better Performance or Better Experience?" used Swype and found that:
No significant difference was found in typing speed between the two input methods
And also specific to Swype, the study "Swype vrs Conventional On-Screen Keyboards: Efficacy Compared" found
Results showed that the prototype Swype was as fast as the standard on-screen keyboard running with word prediction
Both studies noted that users had a subjective preference for Swype, but as you can see, no gains were found versus using a standard on screen QWERTY keyboard.