There's three advantages you get from air launch. One is that your first stage rocket engines can use nozzles that are optimized for vacuum or close to vacuum resulting in better performance through the entire first stage burn. (The RS-68 used on the Delta-IV, for example, has a sea-level ISP of 365s and a vacuum ISP of 420s, which is a pretty substantial difference.[1])
The second is that a launch aircraft at 30,000 or 40,000 feet is providing not just forward velocity but has also allowed the first stage to avoid some gravity loss (to accelerate at 1G at launch you need 2Gs of thrust). It's also allowed the first stage to side-step a major portion of the aerodynamic resistance.
Finally, an air-launched system is not as strongly constrained to specific launch windows. When targeting a specific orbit, you don't have to wait for a specific launch window at the primary launch site (the airfield), you can simply wait until one is relatively nearby and fly to it. This might be a big operational advantage even when it's not a big performance advantage since you can launch your aircraft when you have decent weather over the airfield and the fly to a more ideal spot to launch the rocket. If the radius of the loaded launch airplane is wide enough, this could be a very big advantage.
Even if you add all of these effects up, it's still a pretty small fraction of the 9,000 m/s of delta-v or so that you need to reach orbit. But keep in mind that rockets only deliver a few percent of their launch mass to orbit. A relatively small reduction in the delta-v needed to reach orbit might result in big gains in payload into orbit. In extreme cases, maybe it could double it.
The biggest disadvantage of air launch is that you are seriously constrained in the maximum size of the rocket. The Stratolaunch aircraft can carry about 230 metric tons of payload, whereas a Falcon Heavy weighs in at something like 1,400 metric tons[2].
Comparing stratolauncher payload to Falcon Heavy’s gross weight at takeoff is not really a helpful comparison. FH has a 60 metric tons to LEO max payload, roughly 5% of its total weight. I’m sure someone has done the calcs on the theoretical potential of the Stratolauncher, but it looks like a Pegasus can get 1000 lbs to LEO at a total weight of 40,000 lbs, so same 5% ratio. Seems to be in the same ballpark, and Stratolauncher (would?) use a fraction of the resources.
It depends on what you're trying to launch. It's kind of looking like the next big thing in the launch market is going to be a lot of small satellites in low orbit. This is a market that Stratolaunch might perform well in. It's not the right approach for manned space exploration and probably not for unmanned deep-space either, however.
I'd personally like to see Stratolaunch succeed, but without a dedicated rocket designed to exploit its scale, that's going to be hard. I think Rocket Lab's Electron rocket (a small rocket and a relatively small payload fraction on top of that) would likely benefit greatly from air-launch. On the other hand launching one from the Stratolaunch would be complete overkill, unless you stuck 5 or 6 of them on a rotary launcher or something. An aircraft like Virgin Galactic's White Knight Two would be a much better match for Electron.
The second is that a launch aircraft at 30,000 or 40,000 feet is providing not just forward velocity but has also allowed the first stage to avoid some gravity loss (to accelerate at 1G at launch you need 2Gs of thrust). It's also allowed the first stage to side-step a major portion of the aerodynamic resistance.
Finally, an air-launched system is not as strongly constrained to specific launch windows. When targeting a specific orbit, you don't have to wait for a specific launch window at the primary launch site (the airfield), you can simply wait until one is relatively nearby and fly to it. This might be a big operational advantage even when it's not a big performance advantage since you can launch your aircraft when you have decent weather over the airfield and the fly to a more ideal spot to launch the rocket. If the radius of the loaded launch airplane is wide enough, this could be a very big advantage.
Even if you add all of these effects up, it's still a pretty small fraction of the 9,000 m/s of delta-v or so that you need to reach orbit. But keep in mind that rockets only deliver a few percent of their launch mass to orbit. A relatively small reduction in the delta-v needed to reach orbit might result in big gains in payload into orbit. In extreme cases, maybe it could double it.
The biggest disadvantage of air launch is that you are seriously constrained in the maximum size of the rocket. The Stratolaunch aircraft can carry about 230 metric tons of payload, whereas a Falcon Heavy weighs in at something like 1,400 metric tons[2].
[1] http://www.astronautix.com/r/rs-68.html
[2] https://en.wikipedia.org/wiki/Falcon_Heavy