It depends:
I think the first consideration is the length of the joystick's shaft. If it is a short stick, you have no choice but to top mount it. If the stick is too long, you need to bottom mount it. If it is in the middle, you have a choice.
Secondly, you need to consider you CP's material. Since this is the woodworking forum, I'm assuming you have a wooden, not metal CP.
Finally, there's the aesthetic concerns. If it is a wood CP, are you planning on putting Lexan or Plexi on top? Do you want exposed bolts, or are you strongly against it.
I have wooden CP's (1/2" MDF) with printed CPO's and a 3/16" Lexan top. I didn't want exposed bolts. I have two CP's, one with top mounted sticks, and one with a bottom mounted one.
LS-30's top mount:
The first picture is a CP with LS-30 joysticks. They have notoriously short shafts. I felt I needed to top mount the sticks. I also needed to router the underside to make room for the connections to the switches. I used flat head screws, and the entire joystick sits under the CPO and the Lexan top.
U360 bottom mount:
I made a second CP with an Ultimarc U360. The U360 has a much longer stick than the LS-30. I decided to bottom mount it and routered the space for it. I didn't want exposed bolts, so I countersunk the screws. You need to be careful if you decide to do this, as I've removed material from both sides of the wood at the spots where I'm securing the stick to the CP. I find it plenty strong, however. Note that I top mounted the trackball plate on this CP.