I can only answer for SphinxSEARCH -- dont really know much about the other sphinxes.
It itself doesnt contain features particully for writing reports. Its a general purpose search backend. Just like mysql is not particully designed for reports, but it can be be used as such.
In general think of sphinx as providing a very flexible, fast and scalable 'index' to a database table. Almost like creating a materialized view in mysql.
Because you can think very carefully what data to include in this index. And the index can be 'denormalized' to include all the data (via complex joins if required) - you can then run very fast queries against this index.
Sphinx also supports "GROUP BY" which makes it very useful for creating reports - and because the attribute data is held entirely in memory its generally very fast.
Basically sphinx will be very good to provide the backend for a 'dynamic' and 'interactive' report system. Where speed is required - particully if combined with allowing the user to filter reports (via keywords) - that is where sphinx shines.
Because of the upfront work required in designing this index, its less suited for 'flexible' reports. In building the index, will probably be a number of comprimises, so might be limiting in what reports will be possible. (at least without creating lots of differnt indexes)
short version: lots of upfront work to build the system, for very fast queries down the line.
Sphinx wont really do anything that mysql can't. But using sphinx as part of the system will allow performance to be improved (over a pure mysql solution).