Which version of falcon 4 is best depends on what is most important to you. Falcon 4 Allied Force has the best gameplay for a whole campaign in and only in the MK2 campaign. All other campaigns don't apply because the air resistance is poor due to a lack of barcaps. In the Falcon 4 Allied Force Israel MK2 campaign there is a huge amount of air to air resistance while in BMS 4 there is not. This is because there is lots of barcap missions and the enemy aircraft AI is aggressive. Also in the Israel MK 2 campaign the surface-to-air missiles are smarter. They are hard to take out. The campaigns need you in order for the campaign to be won in the Falcon 4 allied force Israel MK2 campaign. They need you to create missions to sweep out enemy fighters to create a clear path to an airbase.
Even more fun in the Falcon 4 Allied Force is that every mission is challenged by enemy fighters. It is particularly fun when even suppression of enemy air defenses missions are challenged by enemy fighters. This makes clearing out the surface-to-air missiles into path to an airbase very difficult. These surface-to-air missiles are often accompanied by a longer range SA-5 surface-to-air missile. The longer-range SA-5 is hard to take out because it is deep within enemy territory and is well protected by a gauntlet of enemy fighters. This means that the SA-5 remains and that the other SAM sites either turn their radar on at the last minute or turn them on and off. The surface-to-air missile sites turning their radar on and off is very challenging especially when you have a gauntlet of enemy fighters along with it.
BMS 4 is better if you want just want to survive a whole campaign but don't mind the fact that the campaign engine doesn't need you to win. There are exciting missions in BMS 4 in a dynamic campaign. But the dynamic campaign is not as fun because it doesn't need you to win. Also important for an individual mission to be fun are the displays and cockpit features. This is evident in the targeting pod. This makes ground attack missions more fun than in Allied Force because you can see the vehicles you are targeting.
A targeting pod and better cockpit features is not all that BMS 4 has that Falcon 4 Allied Force does not. Surface-to-air missile sites in BMS 4 are harder to jam, especially when it is the older surface-to-air missiles such as the SA-2. There is a particularly fun mission in the start of the Korea campaign in an interdiction mission. The SA-2 keeps firing missiles at you and is very hard to pass through it and complete the mission of interdiction of enemy vehicles. It also has enemy fighters along with the SAMs. This is a very fun particular mission. It has everything. It is one of my very favorites and keeps me coming back. There is probably many more good missions like this in BMS 4.
The disadvantages that BMS 4 has over Allied Force are easy to fix. BMS 4 at its core is a better game and has more potential. Maybe all these problems of BMS 4 will be fixed in a future patch. In which case BMS 4 would be the better game and you would just play that.
Training videos for Falcon 4 are available at simulationscentral.com.