There must be some good in going MAFless others why would so many tuners recommend it?
Firstly, OP has LS1 with slow ECU and low resolution (old) small maf, no OTR CAI and likely the original injectors fitted over a decade ago, so he simply fits replacements, gets mafless tune / new OS and he is going to notice a world of difference. A little conversation with tuner before he begins and he is going to be happy as well.
Short Answer: Mass airflow meters are able to measure airflow. This information is sent to the engine management system and it is able to arrange a precise amount of fuel be injected for that airflow. The problem is that there are many situations where airflow is the same even though the loads and rpms can be very different.
For example 2000rpm at a high load and 3000rpm at low load can have the same airflow. This can cause variations in AFR ratio between the two situations, and these will result in inferior fuel economy, more popping on backoff and less smoothness as the car accelerates at any load relative to a mafless tune that is done properly with all the correction factors adjusted precisely.
The mafs also pickup some turbulence and this creates some very rapid variations in the airflow values it provides the ECM and this results in undesirable variations in spark timing advance.
Complete Answer: The fueling accuracy is much better at all loads if a mafless tune is done properly than can ever be provided by a maf tune. By properly I mean all loads are adjusted to be accurate. This is also dependent on the 02s sensors being in good working order.
The oxygen sensors are able to detect when at anything less than full load whether the air fuel ratios are near 14.63:1 and adjust the fueling coming from the fuel injectors to pull the AFRs closer to 14.63.
However if the O2 sensor trimming system is having to make big corrections because the main fueling is out then this results in the cars engine not running as smoothly and it will also use more fuel because it is less efficient.
If the fueling is accurately shaped and adjusted then the 02 sensor trimming system has less adjustment to do and they can even be even turned off to allow leaner cruising mixtures to improve fuel economy.
The tuners challenge is that air fuel mixtures vary with variations in air temperature, coolant temperature and air pressure.
With old engines running carburettors they run richer when the air is hotter this is because there is less oxygen in hot air and the carburettors jets will always supply the same amount of fuel because there is no correction available. In these modern injected LS1s they should be able to adjust and compensate for variations in weather conditions accurately and always give accurate air fuel mixtures even when at full throttle.
Much of this achievement was made possible because of the modern computer engine management that is available for standard engine management systems in the LS1s. There is an operating system upgrade available for LS1s that improves upon the factory programming, it has extra tables that help take control of what happens to the Air Fuel Ratios as weather conditions change. It also offers the ability to precisely control fueling in boosted engines and even offers throttle percentage based fueling which is useful in engines using 8 throttle bodies etc.
To tune a maf is a simple table with airflow on one axis and the fuel value on the other. This makes for simple tuning. The problem is that mafs are not always accurate and cannot tell the difference between a high load situation at low rpm and a low load situation at high rpm, it is possible for both these situations to be equal in airflow and be covered for fueling by the same value which is a bad compromize.
The maf can also pick up turbulence and can rapidly oscillate the spark timing advance , this is because indirectly the MAF effects the timing advance values. Tuning without the MAF is much more difficult to do properly especially in a E38 equipped engine because the fueling is controlled by an equation which needs to be indirectly manipulated so that fueling at all loads and rpms is accurate. But the advantage is with mafless tuning all different loads and rpms are uniquely controlled.
It's important with mafless tuning that the engine sensors are all healthy and working accurately. The fueling is effected by the intake air temperature sensor, coolant temperature sensor and manifold pressure sensor. It is also important that the intake air temperature sensor is reporting true convective air temperature and is not erroneously reporting radiant heat from the air intakes solid parts. The factory intake air temperature (IAT) sensor is located inside the MAF which is right next to a hose to the radiator carrying coolant. This hose often heats up the IAT and makes it report temperatures well above the real induced air temperature - IAT temps of 80 degrees on a 25 degrees day. The effect of this error are unstable air fuel ratios which are usually on the leaner side of being desired.