As per the linked thread above, the initial numbers looked good. Now that I've accumulated over a month of data, though, the numbers look even better. The graph below largely tells the story. "Render Time" is the time it takes from the moment the server gets a request for a page to the moment it sends it back to your browser. On your end, you'll see some additional delay as resources (images, etc) are transferred from the server, but the render time is a huge part of what makes a website feel "responsive".
Most of the speed increase can be attributed to switching the database to a solid-state drive, instead of the old spinning magnetic platter that housed the database prior. Some additional improvements were achieved by streamlining a lot of the write operations, postponing them until after the page was rendered or moving the database table into RAM instead of on disk.
All in all, I'm really pleased with the increase in performance. As a bonus, the monthly hosting bill is a little bit less as well.