Depending on the hard disk drive you are using and the USB stick you want use the chances are performance wise there isn't going to be much difference. Depending on the model of Pi you have, the USB ports and the Ethernet port share the same controller. This means the USB transfer rate is bottle-necked by any traffic through the Ethernet port.
Also worth considering is all models of the Pi use USB 2.0 connectors. At best through a USB 2.0 connection, (theoretically), you are going to get a connection speed of 53MB/s. (See this post for more details). Generally speaking a modern 7200RPM drive is at best going to give read speeds of around 160MB/s and write speeds of around 150MB/s. Again that's a best case scenario, so you should expect less.
The read and write speeds of the USB drive depends on the type of flash memory that is used in it. A cheap flash drive is obviously going to perform worse in read and write tests. However flash memory can perform on par or better than a HDD. Although you will pay a premium for uber fast flash drives.
To be honest I don't think you will notice a difference between the two. The only thing I would add is if you fill the USB flash drive to capacity it will start to slow down. You are going to be less likely to run into that issue with the 1TB drive.
I can't imagine any lifespan differences would cause you issues. And I'm not sure I could argue one drive is more reliable than the other. If you would like a detailed comparison in this area I suggest you give this page a look.