Once you get past the "make it better and less expensive" part, there aren't a whole lot of non-controversial parts. A few samples:
Decommission obsolete equipment and procedures
Some ground-based navigation equipment (e.g., non-directional beacons in the contiguous United States) is no longer compatible with a modern air navigation system and should be eliminated, along with flight procedures based on that equipment.
Well, those NDBs aren't obsolete to pilots who fly out of fields where that is the only NAVAID, and it is all that is needed to get through an overcast layer. GPS is the long-term solution, but the FAA needs to design the approaches, and an IFR-certified GPS is pretty expensive for an old bug-smasher that just wants to get to VFR-on-top. There are a lot of other technology issues that are cheap to add to a 777, expensive to add to a 172.
Rationally segregate different types of aircraft to optimize traffic flow
Different aircraft types operate at different altitudes and speeds. Large transport aircraft generally fly faster and higher than smaller, noncommercial aircraft. Combining various types means that they all fly at the slower speed, reducing flows into an airport or on a route. Segregation could recapture capacity that is lost today by restricting speeds.
Assume the airlines will want first pick of flight levels. Of course, if it's bumpy or stormy there, they will want to invade someone else's section. ATC already tries to keep everyone moving as fast as possible.
Allocate costs fairly among users
Each user of the system drives certain costs. Users should expect to pay for the costs they drive, but should not subsidize others’ use of the system. The cost of services that benefit the general public, as opposed to the flying public, should be covered by the General Fund.
This is the basis of their entire argument; there are "good" planes and "bad" planes. What complete BS. The entire transportation system of the US benefits the public, and it is almost all funded by fuel taxes. Even the segment of GA that is just rich dudes flying for fun creates an economic impact. No one talks about charging a guy in a sports car as much to use a highway as a semi, and no one asks a guy going fishing to contribute as much as a supertanker to go out through the marked channel.
Does an industry that dumps its pension obligations on the federal government really claim to be the "good" guys.
There are very good arguments posted against this on the AOPA and EAA websites, but some of the more compelling reasons are:
The ATC system is designed around the airlines, GA uses the excess capacity. A small field may have a control tower to handle the 2-3 airline flights a day, it is unfair to charge private planes to use a tower they don't really need. The TRACONs and Class B around big cities are to handle the airlines, GA tends to use nearby feeder airports, but needs to talk to ATC to get under the Class B.
A user-fee system is expensive to track and bill, so is inefficient. Fuel taxes and ticket fees are easy to manage.
The airlines also want a private board of trustees to run ATC instead of the FAA, and the majority of the seats would represent the airlines. How helpful.
The ATA claims to be proposing a "fairer" system, but they are an advocacy group. The airlines don't pay millions for fair, they pay to promote the airline point of view.
