I'm running Ultegra rear cassette with Dura-Ace rear derailer and Ultegra chain.
If I went to Dura-Ace rear cassette, am I going to notice any differences in
shifting smoothness? (Have Ultegra shifters.)

All I know is the Dura-Ace is lighter than the Ultegra cassette. Additional info
appreciates, thanks!

You are not going to notice any difference in the shifting between the Ultegra and the DuraAce cassette. For that matter I often times buy 105 cassettes as they are cheaper and function just as well.

If you have lots of miles on the cassette and chain be sure to replace both at the same time. If you are good about chain maintenance and measure it regularly for stretch and replace then the cassette will last longer.

If you are having shifting issues then fine tune your cable adjustments and really dial things in well. If everything is in tune and your chain/cassette is not worn then replace the cables and housings to improve shifting.