Hey, everyone. I`m wondering what the advantages and disadvantages are of using the different string tensions.

More string tension usually equals more volume and projection of sound, but harder to fret & bend. Less tension, more slinky and bendable action for soloing. Strat Man Dwight

I have subsequently wondered if you might have meant different "tunings", not tension? Later, Strat man Dwight

Course he meant different tunings same as the guy with the floyd rose tuning question answered twice by Dwight Listmayer, before I said use light strings like 9 42.

As the others have said here, lighter strings are easier to push to the fingerboard--good for bending and if your action is high. Heavier strings give you better tone and also help you to play in tune. Even when playing chords, it is easy to inadvertantly bend lighter strings.
You can end up with a guitar that sounds out of tune even when it is not.

If you are tuning down...heavier strings can help the guitar feel more "normal".

When people bring gutars (electric)to me for setups, if they do not specify, I put on .010-.046. This gauge is a good balance between tone & playability. (I love blues and do a lot of bending but those .009s just sound weak and tinny to me.)

Also keep in mind that different gauges put different tension on the guitar--if you change gauges, you might need to have some adjustments made.