amfoto1 Loc: San Jose, Calif. USA

Baseball, daytime, out doors... the 100-400mm for it's 400mm.

Hockey, indoors... between these two I'd want the 120-300mm for it's f/2.8 and because shorter focal lengths are more than adequate.

I actually do use the 100-400 outdoors in the daytime a lot.

Shooting indoors I usually switch to 70-200mm f/4 and, if needed, 300mm f/4... Or in the most challenging lighting conditions, 70-200mm f/2.8 and, if needed, 300mm f/2.8.

For hours of continuous shooting... 70-200/4 (1.7 lb.) and 300/4 (2.6 lb.) are hand-holdable. At around 3.25 lb. for a 70-200/2.8 and the 100-400 II at about 3.5 lb., they're hand-holdable for a while but eventually get pretty tiring.... May want a tripod or at least a monopod.

300/2.8 or 120-300/2.8 are around 6.5 or 7.5 lb. respectively and you'll likely want a tripod for anything longer than a few minutes of shooting.

Having to choose just one... the 120-300mm will be a beast to tote around, but can handle both if you add a 1.4X to it when needed for baseball. For indoor hockey, you probably won't need the teleconverter, may not even use all it's zoom range.

Vector

Perhaps I missed it, but I don't think anyone asked, nor did I see any mention of the body you are shooting with. I've never owned one, but for me, if it's a crop sensor body, I choose the Sigma. I knew someone who shot high school hockey with it on a crop sensor camera. With a crop sensor, you can shoot at the shorter end indoors and longer outside. JMHO!