Depends on the champion. I get Chalice on Taric because it helps sustain pushes or having enough mana to still use Radiance after a team fight. The MR is also helpful and helps to balance out my Armor/MR.
Tear will be better on any character that will benefit from AA or Manamune and imo, gives you better spell spamming abilities than Chalice does.
Chalice is a solid choice on some characters like Malphite who don't really benefit from the ability to transform the item into more AP and/or would like a bit more magic resist. --- "It's like racism, except to only one person." -Todasmile Looking like a nerd is a small price to pay for ultimate power.