I had both for a short time. The Triumph had a more powerful engine and was much more comfortable. The Ducati vibrated more and sounded better, as well as managed the air around the bike better.
Slow speed handling was better with the Triumph, suspension and faster speeds were better on the Ducati. Triumph was very good in town, Ducati did better riding twisty roads. For different reasons neither were great on the highway (Ducati was comfort-challenged, Triumph had bad wind buffeting for my height).
Build quality was noticably better on the Ducati, parts of the Triumph looked like they were bought at the motorcycle dollar store.
After I sell the 851 I might get another bike. A 2002 Daytona CE (in red, only 17 made before factory burned) would probably be high on my list of cheaper used bikes.