This has been updated as of 02/08/2020. As of now, I am recommending using the browser on your phone over the My Disney Experience app.
It seems to be quicker, but this can vary based on the day. I recommend testing out both the MDE and browser and seeing which works faster.
However, the browser still has an advantage that the MDE app no longer has. This is the ability to modify and seek other times for a FastPass you’re currently holding, AND still be able to see what other rides are available. This feature is no longer available in the MDE app as of right now. So the browser has quite the advantage.
All of this is reviewed in the short video below, please give it a watch. If you have any questions, as always please search the VIP group and post if you cannot find an answer.