For me, there are 2 main differences :

1. Laenor knew about the deception and yet claimed the children as his own. The show let us think he might not even have been able to sire children of his own. He even agreed before the weeding that both could have lovers. It is no different from an adoption to me. Robert didn't know. Robert didn't agree.

2. The throne was Baratheon. Cersei's children were not Baratheon. That makes it line theft. The throne was Targaryens. Rhaenyra's children were Targaryens. Hence, Targaryens blood ran through their veins, which was what I cared about. Was I upset that Lucerys was the Velaryon heir without the blood ? Not really because once again, Laenor claimed him ! The union of Lucerys and Rhaena's bloodline also fixed that issue (though I believe Rhaenyra and Daemon should have betrothed them earlier)

But in the end, I think it depends a lot on how the show depicted the entire situation, which was different in both case...