There are some obvious things, like ensuring that your baud rate, parity and hardware flow control are set up correctly. In LV 4, you use a VISA Property Node to set these.
Another common difference in programming between GPIB and Serial has to do with termination characters. GPIB automatically (usually) sets an "EOI" (end of information) bit when you send a command or read a response. Serial doesn't have this.
Instead, the 34401A terminates commands and responses with an end-of-line character.
The hard way to fix this is to visit every place you write and append a "\n" to your command string. And on every read, read until you hit "\n".
The easier way is to enable the termination character with the VISA property node. You'd do this once in
your Initialize VI, at the same time you're setting baud rate, parity, etc.
I hope this helps.
Brian