I too was great fan of wallets like Electrum until I lost my coins due to some hacking and worst part was I can see my coins going but I cant do anything to stop them. There is no way I can recover them. Exchanges like binance are safe in a sense that they provide features like 2 way authentication that keep your assets safe. Nonetheless, if you can take little bit care of your wallet (be it cold or any other) then go for it. Since you have the keys, you own the coins.
I have been using this wallet for a long time and have never had any complaints about it. Probably your losses were not the fault of the developers, but due to your inattention and maybe inexperience. I trust more the storage of my assets in the wallet than on the most, as it may seem, a trusted and safe exchange. As you yourself write that, not your keys, not your money, it only says that all responsibility should completely fall on the owner.