Not certain about DataSift, but we used Gnip and part of the terms was you couldn't display tweets to your users directly off the firehose. I'd imagine DataSift has a similar restriction.
Besides that; neither give you access to private tweets or DMs, so you pretty much have to use the API for a client of any worth.
Besides that; neither give you access to private tweets or DMs, so you pretty much have to use the API for a client of any worth.