It's quite obvious when you actually think about it.
Daenerys Targaryen had to practically learn to ride dragons on her own in 'Game of Thrones'. Despite her "Mother of Dragons" title, she had little experience with dragons, unlike her ancestors who we are currently following in 'House of the Dragon'.
In the prequel, we can see that dragon-riding is thoroughly explored and cultivated. Dragons have riders they bond with; besides, there are crews who are responsible for looking after them and making sure everything is safe. We get a glimpse of such a crew at the beginning of the first episode when young Rhaenyra lands at home after flying around with Syrax.
She also enjoys something she might not be appreciating enough: a dragon saddle. If you think about it, Daenerys had no such thing when she rode Drogon, basically having to trust the dragon and hold on for dear life, as fans reasonably noted.
Back in 2021, 'Game of Thrones' fans would frequently raise the topic of how strong Daenerys had to be to stay on the back of a dragon while having absolutely nothing to secure her.
At some point in 'Game of Thrones', Daenerys even had to hold on to Drogon when he was shot by Bronn – and somehow, she managed to do it with no saddle or seatbelt and survive.
In this sense, Targaryens in 'House of the Dragons' do enjoy some sort of a headstart, as they have mastered the craft of dragon-riding to a point when they can trust the security issues to technology – even the most primitive.
'House of the Dragon' is currently streaming on HBO Max. New episodes premiere every Sunday, with the finale scheduled for late October.