Exact yield of shipboard phasers is hard to determine, due to chain-reaction effect; as result, we cannot precisely determine their actual energy output, since effectiveness of NDF is dependant on density of material fired upon. However, effective yield seems to be one fifth to one third of photon torpedo yield (200 megatons to 2 gigatons per second) against unshielded hull. It still has significant DET capacity, as evidenced by fact that phasers are often used - and are very effective -against shields.
However, we may be able to compare them to disruptors. D 12 was able to destroy 1 058 968 052 to 2 117 936 103 cubic centimeters of Enterprise-D's hull with each shot, depending if only outer hull was damaged or inner too. Actual value is between these two. With having energy required to melt tritanium, we have 1.78 x 10e17 to 1.43 x 10e18 J. That is between 42.54 and 341.78 megatons per shot, which, considering it was outdated BoP, supports my estimate for phaser DET.
Also, 0.06 TW variance was considered extremely small and hard to achieve, giving at least terawatt-range output for Galaxy class starship ventral array.
Another possibility is to use "Q Who" as reference.
Here we see that E-D has started burning throught hull of Borg ship. Without NDF, channel is barely wider than beam itself, which is about the 1/2 to 1 width of saucer's edge. Link2
With height of E-D as measured from here being 142 meters, and leading edge as measured being 7 meters thick, we have beam width of 3.5 to 7 meters. It takes beam 1/3 to 1/2 of second to burn throught that part of cube. By best guess would be that material beam burned throught is equivalent to 3-5 meters of tritanium, if nothing else, then due to SIF. Therefore, we have volume of material melted as being 29 to 98 cubic meters, or 29 to 98 million cubic centimeters.
As seen here, energy required to melt tritanium is 168 to 673 MJ per cm^3. Therefore, energy expended (not counting SIF) is between 4.872 x 10e15 to 6.595 x 10e16 J; due to timeframe, output is between 9.744 x 10e15 to 1.9785 x 10e17 W (2.33 to 47.287 Mt/s).
This is scene at which "Phoenix" destroys Cardassian supply ship. Weapon is not specified, but is shown to be faster than torpedoes, so only option left are shipboard phasers. Distance between "Phoenix" and supply ship is 39 milimeters, with display showing Phoenix' weapons range as being 49 milimeters.
By using calculations done for similar screenshot for photon torpedo page, we can determine phaser range as being 189 184 kilometers. And as said here, it is definetly sublight combat example.
FINAL TALLY: Federation shipboard phasers have effective range of 190 000 kilometers as of 24th century.
In DS9 episode "Return to Grace" we get some notes about Cardassian phasers. At 5:29 we have target being at 400 000 kilometers. At 5:52 order to fire is given. Assuming same speed as in planetary desruptor test we get range of 93 341 kilometers. However, these phasers were not top-of-the-tech: it took long to charge them, and phasers themselves were weak.
