After thinking a while, I chose student designed/mentor built. The reasons: 1) Students have ideas that mentors might not. (The same is true the other way, but students might come up with something that is totally crazy and the mentors might just dismiss.) 2) Mentors are more likely to know how to build x part or know where to get it built. 3) Assuming that mentors are allowed to give feedback/make suggestions, a mentor may spot something that a student missed, then show said student what he missed and what some possible solutions are. If this is not allowed, mentor may just fix it if it's minor, then tell the student later.
My $0.02 worth (worth everything you paid for it

).
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Past teams:
2003-2007: FRC0330 BeachBots
2008: FRC1135 Shmoebotics
2012: FRC4046 Schroedinger's Dragons
"Rockets are tricky..."--Elon Musk
