SharePoint vs teamspace

SharePoint's multi-purpose platform allows for managing and provisioning of intranet portals, extranets and websites, document management and file management, collaboration spaces, social networking tools, enterprise search, business intelligence tooling, process/information integration, and third-party developed solutions. SharePoint can also be used as a web application development platform. SharePoint alternatives for small business are: Office 365, Box, G Suite, Zoho. There are also free open-source alternatives to Sharepoint - Alfresco, Nuxeo, Liferay Portal.
teamspace offers the possibility for teams to work together professionally and flexible via internet. The necessary infratructure for communication, coordination and organization will be provided online by teamspace.

2017 - SharePoint 2016 finally added SharePoint Framework Support to defeate teamspace

One of the big reasons Microsoft pushed SharePoint Framework into general availability in February was to attract more developer talent into the SharePoint ecosystem. And now with the release of SharePoint Feature Pack 2 (FP2), the company finally gives Framework support to users of SharePoint 2016. Framework is a page and web part model that provides full support for client-side SharePoint development, easy integration with SharePoint data and support for open source tooling. The release will make it easier for SharePoint 2016 customers and third-party developers to build SharePoint-focused solutions. Thereby SharePoint is now more customizable if compared vs teamspace

2016 - Microsoft connects SharePoint Team Sites to Office 365 Groups - a new advantage over teamspace

Microsoft is introducing SharePoint and Office 365 team sites integration - the new feature that allows to create connected SharePoint Online team sites in seconds. Here's how the new integration works. When someone creates an Office 365 Group, the service will automatically create a SharePoint team site (with the appearance controlled by the team site administrator) that can include pages, lists, libraries and team news. SharePoint team sites provide a place where teams can communicate, share documents and work together on projects. They are easy to use and enable users create a site for every project the team is working on. Team sites are accessible on all kinds of devices so can be used by mobile workers too.