At the least, in the first option, the generated class for the .aspx page is responsible for wiring up the event handler (and thus, requires the event handler to be Protected); whereas, in the second option, the codebehind class is responsible for wiring up the event handler (so the event handler can be Private).
I'm not familiar with how exactly the Handles keyword is implemented in VB.NET, but it may also affect the timing of the wire-up (I know that wiring up an event in a codebehind's OnInit method will wire up the method at a different time in the page cycle than wiring it up through the markup, and a few obscure cases where that matters).
I, personally, prefer using the Handles method (or using += in C# in the OnInit override). This allows the compiler to verify that the methods exist and don't have to be unnecessarily exposed to inheriting classes. Being compiled also helps when using refactoring tools, looking up usages, etc.