Multiple try-catch or one?

It depends. If you want to provide special handling for specific errors then use multiple catch blocks:

try
{ 
    // code that throws an exception
    // this line won't execute
}
catch (StackOverflowException ex)
{
    // special handling for StackOverflowException 
}
catch (Exception ex)
{
   // all others
}

If, however, the intent is to handle an exception and continue executing, place the code in separate try-catch blocks:

try
{ 
    // code that throws an exception

}
catch (Exception ex)
{
   // handle
}

try
{ 
    // this code will execute unless the previous catch block 
    // throws an exception (re-throw or new exception) 
}
catch (Exception ex)
{
   // handle
}

If I could choose the second I would probably separate this into two functions.

Neither, just use multiple catch blocks for specific exceptions (unless there is just a ton of code in the block and only a couple of lines may throw an exception.In that case I would go with the second method).