This decision really just boils down to personal preference. They both do the same thing when it comes to the rideshare app. Some people may prefer to use a phone because it is smaller and more manageable while some, like me, prefer a tablet since the screen is larger and the phone is free to take phone calls (when you don't have a passenger of course).
Here is a pic of my setup. Unfortunately, there is no Uber bonus or Lyft bonus for going the extra mile and increasing the cost of your rideshare setup. If you are worried about breaking your tablet, just leave it at home and use your phone.
And another photo
I use a special mount, available on Amazon, that slips into the CD player and uses a magnet to hold up the tablet. The magnet is very strong and I have had zero issues with the Tablet sliding out of position or falling.