SharePoint is an ASP.NET application on steroids. Almost everything that works in ASP.NET(3.5) will work in SharePoint as well.
Having said that, the decision to choose between ASP.NET and SharePoint depends on N no of factors .... Requirements, Budget, Skills, Infrastructure, Corporate politics ;-) to name a few.
At the developer level, I think decision can be made on the basis of requirements only.
Also, If you are new to SharePoint chances are high that you would like to develop in ASP.NET :-)
Some points worth to consider:
1) See how complex your database model can be.
It is easy to define and manage data structures in lists as they don't require intervention of a database admin. However, If your application has complex DB design, It may not be feasible using SharePoint. Check out this as well Using SharePoint Lists vs. Database Tables
2) Identify the Features your application will support
SharePoint provide many features out-of-box for which you may have to code in ASP.NET.
If your application need revolve around below, SharePoint is worth to consider:
- Information Portals
- Business Intelligence and Dashboards
- Simple Workflows
- Content Management
- Social networking ( Blogs, Wikis, Communities, People Search)
- MS Office Integration
- Surfacing External Data Systems
- Future Integration with other Systems
3) Cross Cutting Concerns
The majority of web applications contain common functionality that
spans layers and tiers. This functionality typically supports operations such authentication, authorization, caching, communication, exception management, logging
and instrumentation, and validation.
SharePoint provides effective way for managing common crosscutting concerns, such as authentication and authorization, storage, scale, provisioning of services, and governance controls.The value in managing crosscutting concerns in SharePoint is that you don't have to continually reinvent the wheel.
It may be boring to write crosscutting concerns in ASP.NET :-)
SharePoint 2010 and the associated tools promote the increased productivity and accelerated development developers are looking for.