Bitcoin software wallet VS web wallet / Dogecoin hashrate wallet

A browser-based wallet or wallet service is an online account with an external provider where bitcoins can be stored. Examples include accounts on currency exchange Markets, online Services and with ecommerce transaction processors. This definition also includes Hybrid e-wallets.

Warning: When storing your bitcoins with a browser-based wallet on a third-party website, you are trusting that the operator will not abscond with your bitcoins, and that operator maintains secure systems that protect against theft, internal or external. It is recommended that you obtain the real-world identity of the website operator, ensure that sufficient recourse is available and avoid services that do not use an offline wallet (cold storage) for bitcoins that are not needed for daily transactions. Storing significant quantities of bitcoins on third party websites is not recommended. (Note: some Hybrid e-wallets might be exempt from this warning, and adequately safe for storing large amount of Bitcoins. In any case, do your own homework and learn how each site operates).

Benefits

An account with a wallet service can generally be established in just minutes.
Since withdrawals can be made to any Bitcoin address, simply using the withdrawal feature to withdraw to an address that is not yours is functionally equivalent to sending a Bitcoin payment when running the Bitcoin client locally.
Some services offer instant, internal transfers. This allows transactions to complete without having to wait for block confirmations.

Things to be aware of

When bitcoins are stored online, the provider retains full control of those amounts. You are trusting a third party to maintain your Bitcoin balance on your behalf. In comparison, if you run the Bitcoin software yourself, you are in full control of your coins so long as the wallet file stored on your computer is kept secret and secure.

Other relevant things:

You typically have less anonymity with respect to those who run the online wallet site.
If a payment is made from an online wallet, the last-sent-to address (often incorrectly called a 'from' address) is an address for the wallet provider and not an address reserved specifically for the sender. This is because the wallet service provider may service the payment from any coins in its possession - your balance is not associated with any particular coins, any more than your balance at your local bank is associated with any specific bills. Thus if the recipient were to "return" any bitcoins to the last-sent-to address, the sender would not receive those bitcoins — but last-sent-to addresses are completely unsuitable for that anyway.