White is a bit hotter. (I tend to think of peppercorns as pungent, though. Chilies I think of as hot.)
Peppercorns for the white varieties are allowed to mature longer on the vine. The outer black shell is removed. To me white pepper's flavor is somewhat wine-y. I use more white pepper than I use black and green combined.
White pepper is the
nut, imo, for potatoes, especially mashed - or in others with lots of dairy or fat included.
In addition to the items j notes, I use white pepper in many rubs and seasoning blends. My version of Quatre-épices (a spice blend used in French cuisine): Combine 1 T freshly ground white pepper with 2 t ground clove, 1 1/2 t ground nutmeg, and 1 1/2 t ground ginger. This is a favorite of mine for chuck for smoke/braising or prior to browning for oven braising.
White pepper, imo, works especially well with cooked fruits too, like in fruit-based chutneys.
For a broader pepper flavor combine white and black pepper; for that plus high notes add some green to the blend.
This rib rub combines the three. It's also quite good on beef, as the ingredients suggest, though for beef I cut the sugar to a teaspoon or two. Nice on flat iron and tri-tip.