Personally I prefer to be sent a full email thread over a message in chat, because

a) I can ignore it until I have time to look at it

b) You can see who else has already been involved in the conversation - seeing a fellow team member being involved can help avoid falling for situations where someone is trying to work around one of your colleagues who's already told them they can't have what they're asking for.

c) The chat message is from an individual, so you only get their interpretation of what's happening - if there's an email thread then there's going to be multiple people involved, each with their own perspective.