FIrst of all, why should a blackberry be less fit to daven from than a siddur? Is it because of the dreaded “T” word?
The only real issue is one of “tarud,” i.e. a lack of kavanna. It says that one should not hold tefillin while davening because he will be worried about dropping them and hence not concentrate properly. Most poskim extend this chshash to anything valuable so it might be better to avoid holding your expensive phone during shmoneh esrei even to daven from it. Personally, I daven by heart.