I'm using Blockchain wallet because I do not want to download anything to my computer or phone. Blockchain work on mobile browser too, I do not understand why some people download the application.
it's safer to hold your coin in local wallet that you have 100% access than store in 3rd party wallet
especially if you have large amount of coins
if you decide to use online wallet like blockchain, i suggest you to activate 2FA for security reason
and like above user said, blockchain known for their downtime (occasionally)
if you need to send bitcoin in hurry and at the moment blockchain is down, what will you do?