Event handlers are a great tool for managing errors and other events that occur during the execution of a package run. Using event handlers can however add additional time to the run of a package. Depending on the event that is selected it could cause more performance issues than others.
For example, if you have the OnInformation event selected then the package could fire off the event dozens of times during one run, but when you have the OnError event selected you will only see the event fire off on the failure of a package or task. So be very careful with event handler usage.
A side note on event handlers is they can be disabled. From the event handler tab you can open the properties menu and change the Disable property to true, which will disable the selected event handler. To disable event handlers all together in a package change the package level property called DisableEventHandlers to true. Try it out by using the OnInformation event before and after disabling to see the performance hit.