There are two main reasons you might opt for the Roku 1 over the new Streaming Stick. One is universal remote support. Standard IR-based universal remote controls won't work with the Streaming Stick because it's hidden behind your TV, so the Roku 1's traditional box is an advantage in that case. (However, Logitech has said it may add the ability to control Roku boxes over Wi-Fi on products that use the Harmony Hub, such as the Harmony Smart Control.)
The other reason is if you need analog analog video output. The Roku 1 is now the cheapest box with legacy analog connections, so it will work an older TV that has a composite video input (i.e., the yellow video port.)
Otherwise, the Streaming Stick looks to be a superior product in just about every way, especially if you're ever tempted to grab your Roku and bring it to a secondary location, like a relative's house.
Roku boxes compared
For a deep dive on the full Roku experience, check out CNET's full review of the Roku 3. Below is a breakdown of Roku's full product line.
Roku 1 ($50): 1080p video; HDMI and analog video outputs.
Roku Streaming Stick (2014) ($50): smaller form factor, adds RF remote and dual-band wireless, YouTube support out-of-the-box.
Roku 2 ($80): adds Wi-Fi Direct remote with headphone jack, YouTube coming later this year.
Roku 3 ($100): adds dual-core processor, motion control remote, Ethernet jack, USB port, SD card slot; no analog video jacks; YouTube currently supported.