One huge difference is of course that the Store Apps supports Universal Apps, where you can easily share almost all all of the code across WP8.1 and Windows 8.1 (including XAML).
But it is Worth noting that there are several features which some apps might require which is only available for WP8.1 Silverlight apps, such as:
- VoIP support
- Act as Lock screen background provider
- Act as a Lens app
- Let app extend search results using search extras
- Provide ringtones
And a few other listed here along with a feature mapping from WP8 to WP8.1 Silverlight and Store Apps: http://msdn.microsoft.com/en-us/library/windowsphone/develop/dn642486(v=vs.105).aspx
If you are starting a new app and will not need any of these features a Store app is probably the better choice though.