My take and a well established trader would tell you that the mainstream wallets are not the best place to put your money, in fact tokens come up missing or hacked, accounts can be compromised or lost. These are not all just hypothetical but have actually happened. Main reason why like 3 of steamit's rules are do not loose your password, keep it safe. Once your account gets big you do not want that vulnerable in the network.
With paper wallets you can go offline ( like side chain) and take your money off of the network where it cannot be hacked. They are now files taken from the public server of files that happen to be information about your wallet and it's whereabouts. You do not want to enter or scan the contents of your wallet into a device with a virus, that can also make you more vulnerable to attack. Using computers that are not broadcasting or public are good for this type of thing.
Also flash drive can back up your wallet but the same rules apply, both of these are better options than the mainstream wallets, they should only be used for small amounts and trading, I keep mines as low as possible until its time to trade.
Honorable mention bitcoin.org as we all know has the original wallet Bitcoin Core, this comes with the entire block-chain downloaded on to your computer, and a transaction fee paid to the miners. If you do not pay it will take longer to confirm and go through to where you sent it. And your going to need alot of extra space and time to download it all onto you laptop or desktop.