The answer to the question "Which solution is better to use, Box vs. SharePoint?" all depends on how the business wants to use the applications. SharePoint and Box claim to be perfect for feature-laden cloud storage for file collaboration, synchronization and enterprise content management (ECM). While they each offer standard features like file upload/download, security based sharing, browser-based document preview, synchronization with desktop files and standard workflow for review, approval, and access, there are a few ways these solutions differ, especially when Office 365 applications are considered.
SharePoint integration with Office 365 applications and features will help make the decision for many organizations, especially when an organization already has its investment solidly in the Microsoft stack. And SharePoint integration with customer relationship management (CRM) may also sway decision. But all of the integration and added features in SharePoint have caused administrators to evaluate impacts on user experience and utilization of capabilities return on investment.
Desktop synchronization when users work offline and reconnect to sync updates is another issue. Office 365 OneDrive has had problems with reliability with its interface (not unlike BoxSync issues) and the out of box behavior of Office and it's multiple saves per session can cause unexpected results. The in-browser editing will be an important feature for SharePoint that Box cannot deliver, but once again reliability will determine which solution is best for users.
Another important difference is how data and information management and governance is handled between SharePoint and Box. Governance requirements like records management and retention, e-discovery measures, privacy policies, and compliance standard adherence are all points to consider when choosing SharePoint over any other solution. The use cases should also consider how the files need to be shared and via which types of devices.
Browser issues, OS incompatibilities, performance and responsiveness challenges and poor support have also been reported on the Box side, but SharePoint wrestles with some of these same performance glitches on occasion as well. Some of the issues are inherent to the cloud and are affected by constraints like a user's hardware configuration, system management and connectivity.
There is plenty of SharePoint functionality that Box does not offer including general features like cascading permissions for child folders and files, metadata based views, advanced search capabilities, document versioning and real time, collaborative editing, workflow, apps like calendars, discussion boards, wikis, personnel directories, task lists, iframes, etc. Box cannot replace SharePoint for corporate intranet, community and collaboration capabilities and is not nearly as open as SharePoint to development to match business requirements. Any consideration of migrating from SharePoint to Box needs a determination of which features need to be migrated and which SharePoint features prospective Box users can live without.
Box really is mostly about document storage and was created to compete with the likes of DropBox, Google Drive, and other online sharing platforms, instead of becoming a SharePoint and Office 365 One Drive killer. But Box is meant to be more compatible with other devices and platforms, including Microsoft Office 365, Googl Apps, AWS, Salesforce, Netsuite, Docusign, Adobe, etc. This is one capability where Box excels over SharePoint and other online content management tools.
When it all comes down to it, the choice between SharePoint and Box all depends on business and user requirements. Cost could be a dealbreaker for some organizations as well. The cloud factor has certainly disrupted those requirements, but the core needs of the business and its users really haven't changed much and if they have it's because tools like SharePoint have evolved to do more to increase utility and ROI for business applications and tools like SharePoint.