Hi budd and welcome to a great game, both the PC and board game varieties. It's my personal favorite tactical wargame system so I couldn't recommend it more.
Classic AP mode versus Persistent AP mode is an interesting question. I know in the BoardGameGeek forum where they cover the board game (obviously), people are biased towards the Classic AP system as one would expect. Both have merits and I've played with both systems extensively. I feel at the end of the day , Classic AP is a more tactical system and rewards long term planning. You have to be thinking ahead and what you want to accomplish and then execute that plan. When something unforeseen happens, you have to decide the best way to deal with it and there are many, many options (most with pros and cons). With Persistent AP mode, you really don't have to deal with this since it has absolute flexibility and there is rarely if any, repercussions to switching on and off units.
For example if you have a LMG34 as the Active unit and a Rifle squad covering its flank that is "Fresh" (meaning hasn't activated yet) and your opponent unexpectedly launches a flank attack on the LMG34, in Persistent Mode you would simply activate the Rifle hopefully kill the attacker, and then go back to activating the LMG34.
In Classic AP mode you would have to make some choices. You could:
1. Mark the Active LMG34 unit spent losing its remaining APs and Activate the Rifle squad with it gaining its full APs to use.
2. Keep the LMG34 active and decide to use an Opportunity Action. This would allow you to perform one action with the Rifle squad and then it would be marked spent while the LMG34 was still the Active unit. It's inefficient but represents the difficulties of command and getting a unit to change tasks on a fly.
3. Keep the LMG34 active by using a Command (CAP)Action. This means spending only CAPS to make the Rifle fire while preserving the LMG34 as the Active unit and also the "Fresh" state of the Rifle unit. Of course you need CAPs do do that and there is never enough around to do everything you want.
4. Keep the LMG34 active but doing a Card Action which again allows the Rifle to act without changing either the LMG34 or its status. A card could also negatively affect the enemy unit, something like "Marked as Used."
As you can see, there are many more choices and combinations of what can be done using the Classic AP mode over the Persistent AP mode. I do know the PC allows the Persistent Mode whereas the board game designer didn't think it would work in a board game setting.
It does come down to personal preference so in that way, there is no wrong choice. However the two people I know who came to this game by way of the PC game and Persistent AP mode who I taught Classic AP mode to, prefer it and have switched.
Finally here's a good explanation of how Classic AP mode works, straight from the board game rules (latest version):