It is not a mutually exclusive decision. I used Swampdragon's serialisers with Pusher (and hopefully in future releases Swampdragon will share its serialisers with DRF as well).
In terms of ease of use, Pusher is easiest to setup as it is a PaaS service so you don't need to install anything. Swampdragon has a slight advantage that you can run it locally without any outside dependencies, which is nice for development.
Scaling and cost, well it depends on your current architecture. Swampdragon you'll need to scale out/maintain your own Redis and Tornado servers whereas with Pusher it's a fixed cost and you don't have to worry about scaling/bursting etc.
A pattern I've seen personally is people start with self-hosting until they reach more concurrent connections than a single server can comfortably handle and then switching to a PaaS service like Pusher.