In commonly-used developers, Delta 400 tends to produce relatively lower shadow-area contrast and relatively higher highlight-area contrast compared to HP5 Plus. This can make the negatives more difficult to print - that is, to maintain detail in both shadows and highlights within an overall tonal scale that is pleasing.
If you must use the Delta 400, be careful not to expose it too little or to develop it too much. As a general principle, that applies to all films. But as you stray from optimal exposure and development - or if you're not yet sure what optimal exposure and development are - you'll get into trouble more quickly with Delta 400 than you will with HP5 Plus.