One of easiest way to create and access Ethereum and erc20 token is MEW web interface. My question is , is it safe to keep big amount in MEW or better not to rely on it.
first of all you need to understand what Mew actually is. MEW is a tool to allow users to create and load (open) their ethereum wallets. but mew itself does not control your wallet, it doesn't store your private keys. and the coins/tokens you view in your wallet using mew interfact are not stored in mew. but they are stored in your wallet and in your private key..
now about safety of using mew. yes it is safe. it provides you a lot of possiblities to load your wallet. it always gives you the warning to not load the wallet using your private key. always use ledger, metamask or a third party tool to load your wallet. so yes. mew is very safe
I use MEW only for transactions but it also depends on each one because now to send ETH or tokens, there can be many things including applications, but at the core, your private key, SEDD, is the most important phrase you keep safe because only you are the one who know about then i think it's very safe.
As @ATriz said now a lot for ETH storage from Ledger, Trezor etc depending on which one you prefer but all of that very secure and we only differentiate which interface is preferable.