Feeds vs. Aggregator for rss
Even though the module's name is 'Feeds' , it can import CSV, XML and other types of data too. Also, you can attach them to a stand alone form or a node type form. 

The basic difference between aggregator and Feeds module is, how it stores data. 

Aggregator module stores categories, feed URLs and imported data in its own tables. You will have Views support but it cannot be extended like nodes or such entity. 

Also, you will not be able to map data. It's almost a fixed structure, like title to title, body to body, etc. 

But in case of Feeds, you can decide what you need. 
You can build a standard feed importer that maps feed item's title to node title and contents to a body field. But you can also be radical by mapping to other fields. 

You also can use different entities as the target. 
It also has 'pubsubhubbub' support which Aggregator doesn't support. 

Both modules uses cron to fetch data. 

Use aggregator if you want to show contents from few RSS/atom feeds in a simple block. 
For all other cases, I'd recommend Feeds module.