That depends how many coins and what coins you have. I would recommend to store as many coins as you can in wallets by the core clients and the unimportant coins on other wallets. I have 6 main coins that I need to have on a wallet and I usually make private keys in the core wallet software and import them to a wallet like electrum (never make an electrum wallet by electrum itself). For some I only hodle like IOTA i just save the keyphrase/private key.

I do trading on markets so I keep a small amount on the markets and when I want to put things to savings I send it to the public keys that I have stored without need to a open wallet with a private key.