Hi Lyle,
You can find the differences between this collations here:
http://forums.mysql.com/read.php?103,187048,188748#msg-188748
Summing it up, utf8_general_ci is a simpler collation, which is faster and simplifies the text, as in the post above say:
For example, these Latin letters: ÀÁÅåāă (and all other Latin letters "a"
with any accents and in any cases) are all compared as equal to "A".
utf8_unicode_ci is slower than the general but offers a extended multilingual support
If it depended of me, i would clearly choose utf8_unicode_ci, although it is slower, for two reasons, multilingual support, and not losing data in possible migrations or upgrades. (If you have A in a table, it doesn't matter the collation used, but if you have a unicode table with Á and you convert it in general, you will reach to A, which to me means to lost info)
Just my two cents 
Regards
Joined: 01/23/2008