From what I can tell the iPhone (ios 5x) does not have a feature equivalent to the Blackberry "Sound Profile". Nor do I see an app that will provide this.
For example, on the Blackberry I could set a sound profile called "Loud" which would have the individual ringtones, vibrate and volume settings I want for when I'm in a noisy place. I could have another setting called "Quiet" with the settings I want in a quiet place, a setting for "Silent" etc. Then I could simply select which Sound Profile I want to be in effect. Very useful, very convenient, very easy to use.
The iPhone has the ability to set global sound parameters (volume, alert sound, ring tone) BUT does not have the ability to save sets of global sound parameters for instant retrieval and use by the user. This is, in my view, a shortcoming. Not a show-stopper, but a shortcoming.
Not to compare Blackberry devices to iPhones, but the "sound Profile" feature in the Blackberry is very useful and I wish Apple would provide ths feature and urge them to do so.