The serial mechanism of the POINT ASCII modules and the built-in serial port are totally different. Instead of having the ASCII serial port instructions (ASCII Read, ASCII Read Line, Clear Buffers, ASCII Write, ASCII Write with Append) you have an Output image buffer into which you place serial data and a length, then change the value of a transaction counter to trigger the writing of the data.
The Sample Code would be reference material only for implementing Modbus on a POINT serial module.
If it were my system I wouldn't hesitate to use the 1782-JDM. In volume I'm sure they're comparable in price to the 1734-485ASC. I wrote some widely-used technotes on the SLC-500 and 1782-JDC almost ten years ago and have a great deal of regard for Western Reserve Controls.
What is the Modbus device you need to connect to ? Do you need to both read and write Modbus data ? Is it a multidrop system with multiple slaves ? How many different Modbus transactions do you plan to use (holding register read, coil write, etc) ?