How powerful GCS phasers are:
There are two primary families of evidence relating to phasers. First, we have numerous incidents against inert targets ("The Pegasus," "Legacy," "A Matter of Time," "Inheritance," "Masks") all of which suggest that phasers, used on carefully
controlled [low] settings to limit collateral damage, can put out a hundred megatons per second or so. Extrapolating to combat settings leads us to estimate phasers can put out roughly a gigaton per second of effective material-destroying yield (placing disappearance equivalent to energetic vaporization.)
Second, we have the power generation evidence. From "The Sound of Her Voice," in DS9, we see phaser power banks significant relative to warp engines for an over-armed ship; in "Best of Both Worlds," we know that the phasers cannot handle the full warp core output. Knowing that phasers are significant but not overwhelming in comparison to other systems, we are best suited suggesting that phasers use up to 1-10% of what the warp engine puts out.
Requirements for warp fields and warping away from planets/suns place the warp engine's peak power usage at around a hundred gigatons per second, possibly even more.
Between these two families, our most plausible compromise is to place GCS phasers at around a gigaton per second in both
effect against targets and in
power required to use, i.e., that phasers are about as powerful as they look. I'm pretty sure they're between 1-10 exawatts; individual phaser "blasts" seen in combat, which often last a significant fraction of a second, probably reach an exajoule.
How powerful the photon torpedoes on a GCS are:
We have a lot of evidence indicating these are antimatter warhead devices. They are variable yield, and can be set anywhere from "firework" to "surface bombardment" yields. Their shields may absorb energy that is also released upon detonation.
Various detonations, especially "Skin of Evil" and similar incidents, suggest that the top yield of a photon torpedo is perhaps around a gigaton.
Views of the interior of a photon torpedo, and the much less energetic effects seen, suggest that standard [anti-shipping] loadouts are probably around 100 megatons, possibly even as low as the figure given in the TNGTM.
How powerful are the turbolasers on an Imperial Star Destroyer
From the movies
It is difficult for us to judge this well from observation in the movies alone. Depending on how the asteroids in TESB are scaled, the bolts seen fired could be sub-kiloton - or multi-megaton - if they're vaporizing the asteroids.
Impacts against other capital ships in ROTJ (and by similar ships in ROTS) could be against unusual hull materials, be partially blocked by shields, et cetera.
Most particular, however, are three things.
- Fighter-range ships around a millionth the size have gigajoule range beam weapons that fire multiple times per second. See Slave I.
- Thermonuclear weapons are used in combat, although just a couple missiles will not hurt a capital ship.
- Missiles are rarely used - almost never by capital ships.
From this, and my preferred estimate of ISD power consumption, my preferred best guess is that Star Destroyers can put out up to 10 megatons per second through turbolasers in their peak combat performances.
From the movies+EU
In spite of the outlier ICS, it becomes more difficult to place ISD firepower in the multi-megaton range, because volleys of relatively low yield proton torpedoes fairly consistently bring down capital ships. This makes it especially difficult to believe that capital ships can battle each other for significant lengths of time, even when we consider the much higher peak wattage of a nuclear device (1/1,000,000th second) compared with a similar yield turbolaser bolt (1/100th second) in overloading shields.
When I consider the whole of the EU, I am inclined to revise my estimate towards the mid, rather than high, end of the range in which nuclear weapons are useful yet not preferred. My best guess becomes a megaton per second peak turbolaser output - still enough to bombard a planet into ruin in a reasonable length of time, and with poor capital ship accuracy, mean the proton torpedo attacks don't have to invoke too many ridiculous assumptions.
Notes
I realizes this stretches the visuals of impacts seen on ships, especially in ROTS, but also in some DS9 battles. We can explain some through tough hull materials, for which we have substantial evidence in the Trek case.
(EDIT:
An older poll/thread some might find interesting.)