The main reason you'll want to send Kimahri down Rikku's path is so you can steal a lot of Lv. 3 Key Spheres from Biran and Yenke, they are quite rare at that point in time and definitely useful to get in that battle. Also, whoever you send down the first part of Rikku's grid gets an abundance of HP plus some pretty good stat boosts (not to mention the +8 STR at the end). So yeah, Rikku's path is definitely not a bad idea.

Unfortunately, there's no way to quickly cross over to Auron's path (if I remember correctly, you have to take quite a detour) or it wouldn't even warrant a discussion.