All online wallets in my opinion are safe, I have also used an online wallet for a long time and have never experienced any problems, a secure wallet all depends on you in managing it and maintaining a password or private key.
Do you know that not all online wallet are decentralized, sometimes centralized like xapo, etc which we must register using email. This also an online wallet but not secure. So I think all wallets which we keep the private key are safe, not all online wallets
So, electrum should do the job for bitcoin wallet and for Ethereum we can use the official one or maybe the MEW wallet can do the job. MEW is a better choice according to me as you don't have to download the blockchain for using the wallet whereas in the official wallet you have to download the entire blockchain at the time of first use, in later uses you just have to synchronize the blockchain to transact. But, online wallets should be the choice for those who can't have a backup of their software wallet as if you loose your wallet file then everything is over and you can't recover the address in which your funds were present.