There is a 3rd alternative...
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Why choose Basecamp or Bitrix24?
Both tools have similar features such as add-ons, roles management, contact management, chat, file sharing, mentions, and groups/channels. However, Basecamp offers graphic personalization, custom domain name, workspace and user activity, and 1-1 video call features, which Bitrix24 lacks. On the other hand, Bitrix24 offers features such as polling, group video calls, screen sharing, audio call, recording, online document editing, newsfeed, notes-taking, calendar, task management, and "do not disturb" mode, which are not available in Basecamp. Finally, Bitrix24 offers training resources such as on-site, online live, docs, videos, training webinars, and dedicated CSM, which Basecamp does not provide.