~snip~
But to answer your question in the way it is, i'd say it is safer in the former, the only way the person will lose their coins is if anything takes Binance down, but in the latter, the person is susceptible and would prolly be hacked quicker, based on how they use their device and general security practice.
If you keep your coins on a centralized exchange, then there are several ways you can lose them :
1. CEX is hacked and that is something that no client can influence - but one can still hope that the company will compensate him one day.
2. The client loses his coins because he entered his login data in a phishing site - he cannot hope for any compensation except to report the case to the police and for the police to officially request the attacker's IP address and all other information that could help in the investigation.
3. The client loses his coins because his device is infected with clipboard malware, which results in a transaction that sends coins to the attacker's address. There is no compensation or even the possibility to detect the attacker, except for a complicated and sophisticated blockchain analysis that may not give any results in the end.On the other hand, someone who loses coins and used a hardware wallet can become a victim of the clipboard malware described above, or a seed stealer in the sense that he enters his seed into a fake wallet. In both cases, we can say that the game is over for such a person, because even though he can report the case to the police, the chance of returning the funds is almost nil.
As strange as it sounds, a hardware wallet in the wrong hands is sometimes worse solution than storing coins on CEX.