using my own - I can always implement my own strategies that way. I always saw Pokemon Stadium as an extension of the gameboy games. After you beat your rival and became champion, you take your team to stadium and really test your skills.
I have used both. When I was young I used rental Pokemon to complete R-1 gym leader castle and a few cups. Later, I trained my own team up and completed the entire game (except for the trophy place). I like using Pokemon I trained up rather than using rental.