AFR or Fuel VE Table Tuning

I would like to know what is the difference or the advantage to tune by AFR or Fuel VE table.

When you use the term 'AFR' I think you're actually referring to a VE fuel model. In this sort of fuel model the ECU provides a VE table. We tune this until the measured AFR matches our target. once that's done we can then make AFR changes by simply adjusting our AFR target table. This sort of ECU can make it a little easier to get an engine up and running for the first time, and it has some advantages when it comes to running flex fuel as the engine's VE doesn't change (much) when moving from pump gas to E85.

The other sort of fuel model we see is 'injection time' base where the fuel table is directly requesting a specific pulse width from the injectors.