Has 'Salesforce1' made it obsolete? Or there is still some functionality which is supported by only classic & not Salesforce1.
Yes, as per the Salesforce1 guide, you should still use Salesforce Classic if you need offline support. The guide states
Salesforce Classic remains the best option if you need offline support, - use of Custom App (not Salesforce1 Platform) to configure and control complex offline behavior (Mobile SDK only)
This is because Salesforce1 does NOT provide any offline support at the moment. Based on the Spring 14 release notes and the Intro to Spring 14 webinar dated 15th Jan, it's not clear as to whether the offline support will be included anytime soon. This has also been discussed here.