Basecamp is oriented more towards project management where you are building your communication around project/tasks and tracking projects/tasks. Slack on the other hand seems more like an enterprise communication log/archive and a place that brings all communication in disparate systems to one common ground, this way you just need to go to one place to find status about anything and everything. It is one place to talk about everything in a company. You can compare Asana as a competitor to Basecamp and hipchat as a competitor to Slack.

In short you cant just use Slack to replace Basecamp and you cant use just Basecamp to do what Slack provides.