I have worked on both. Agile & Waterfall.
When i joined the team, the team was following waterfall, Each enhancement, feature request was considered as a Change Request (CR) and one CR is assigned to an individual with a given deadline of 1-2 months depending upon the importance and type of work required. No daily statuses are required , you meet your team lead/client if their is any issue and everything is with you until you finish the requirement. The responsibility of complete CR is on you (Security of code (Manual, Automatic WebScan, Checkmarx, Sonar Cube), Performance of code, Code Review (IQA,EQA), Unit Test and at last Deployment). PS : Deploying the CR is also the responsibility of person working on it (Team is always ready to help. But, at last its your CR and you are the one leading everything).
After 1 yr we started migrating to Agile, and now from almost 1 yr we are following Agile.
In Agile the earlier CR is divided into small tasks (User Stories, Defect Stories, Data Management Stories) and assigned to individuals. Means now the entire team or many people are working on same CR. Deadlines are short and for user-stories (2 Weeks). Their are separate members who handle code security, and deployments. So, we only need to focus on development (+ Code Review, Test Cases :P ).
Their is daily status call and you need to tell the current status of US and issues you are facing.
Well for me , Agile works best. The same work is divided and completed quickly.
Tools : We are using in-house developed tool for all Agile activities. ( Used by fortune 500 companies :P ).
PS : Their may be certain things which we follows but, i have missed or may have certain deviations from perfect Agile .