Keep your coins in exchange if your are a trader because it will save the deposit and withdrawal fee so you can get more profits but it is risky to store it in the exchange since the chances of getting hacked is more.
Keep you coins in wallet if you want to keep your coins securely for long term but some wallet don't have custmoizable fee so the fee will be high if the high traffic in the blockchain.

Any sane coin holder would choose to have a hard wallet for safekeeping. The reason is simply because you control your own private key which is a lot secured than those exchange sites. Also, during hard fork of particular coins, your hard wallet will just need some updating and you will be able to gain the forked coin. But it also depends on your preference, if you are going to use your coins on a daily basis say for trading purposes and then convert it into fiat for your daily expenses, then I suggest have your coins stored in an exchange site for easy liquidation.

The best for me is using wallet most especially when you want to hold your coins in long term it will be more secure. From their your coins will be more safer and investing using wallet will always be the best than giving your coins in the exchanging site. If you will read more and more you will see that most of the answers will be in favor of wallet.

If you would like to buy some coin for long term investment like more than 1 years much better keep all that coin in personal wallet that we have the private key so we have full control with our money. But if you buy the coin for day trading you can put the coin in some exchange, and to minimize the risk use more than 1 different exchange, because now many case about hacking of exchange.

Just remember one thing - while you hold your coins on exchange - it means that you store you coins on somebody`s wallet. It is not safe at all.

If you are holding coins  for the longterm, it is imperative you keep the coins on your secure wallet and then safeguard your p[rivate keys and back up. i would prefer an hardware wallet or utilise the various options of wallets

If you want to exchange it now, it will be better if you send it to the exchanger, but if you want to wait for the price to be high, just save it in your wallet, because you can access it at any time.

It is upto which exchange it got listed, If i am trading on that coin then i leave them in exchange, if not i just keep in my wallet for safe. Because keeping coins in exchange is risky. Only daily trading coins are to be kept in exchange.

It is advisable to keep your coins in a cold storage or hardware wallet. Cons of keeping your coins in an exchange is that the site might get hacked and you might lose your coins.