They do the same thing, but all a bit differently. I use direct routing for quick switching, and for temporary routing to hardware, or for printing stems. You cannot send level with direct routing, it is just switch (or split if in summing mode). Also there is no pre fader.
For parallel processing send level and pre fader can be handy, so you can use send to fx or send to group.
If you use direct route, you disconnect previous routing, so it is handy if you want to quickly reroute signal, but then you just switch it back when needed. It is like a switch. (Unless you use summing mode, then it is like a split, same signal goes to all outputs.)
Hm, I explained it above. Summing mode is like a signal splitter. It sends the same signal to multiple outputs at the same time.
If you have summing mode disabled, then selecting new direct output will disable previous one. But when you enable summing mode, then selecting other direct output will keep previous one enabled. So you can have 8 simultaneous direct outputs active in summing mode. Without summing mode you can have only one direct output active at the time.