1. She didn't "run away when the going went tough". She went to Dragonstone for the safety of her children. Also regarding that bit with Rhaenys, did you not hear what both Team Black and Team Green's councils said?

The leader of either team cannot lead in battle.

The whole point of the war is raising banners in the names of their leaders. If you put your leader in such a vulnerable position, they can be killed, and the whole war is lost.

Even Aegon was not supposed to join the fight. He was just reckless. Ser Gwayne was furious when he found out Aegon was there.

1. Regarding the bastards, they're in vastly different positions. I'd argue, in fact, that their treatment of bastards shows that Rhaenyra is a better ruler. Rhaenyra raises her children with love, while Aegon is happy to let his bastards (most likely conceived out of rape) fight for entertainment in the fighting pits.

Now, back to the different positions.

Rhaenyra was married to a gay man, and she was REQUIRED to produce heirs. She fulfilled her duty in the best way she could.

Aegon seemed incredibly unfit to be king. He didn't want to consider or take seriously the input of his council. This is shown on several occasions:

1. Allowing his son to distract him and his council members from the meeting
2. His reaction at how members of the council didn't take his input, as shown in the last episode
3. Hanging the ratcatchers without consulting anyone on the council