I thought that they both get a copy of the card. During the trip to Kyoto Negi uses his copy to try and telapathicly (awful spelling) contact Asuna but because she wasn't told how to use the card that he gives up and uses his cell phone.
Though in the later books he doesn't have to use a card, only the card holder does that...
e.g. His practice date with asuna during the festival
As for whos picture appears, it probably has to do with the magic circle that Kamo draws on the ground. Part of it probably determines negi as the leader figure in the contract.
Imagine if you will a garden with a beautiful blossom tree and a koi pond...
...Next imagine me drowning you in that very koi pond...
That is the power of feng shui...
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