The arguments for ECC are (a) it is much more efficient than RSA so you can use stronger keys at less cost, (b) ECDHE is so much faster than DHE (over the integers mod Z) that ECDHE becomes practical in situations where DHE wasn't, (c) it is in NSA Suite B, (d) the major crypto libraries already implement it.
The arguments for AES-GCM: (a) AES-GCM and AES-CCM are the only standardized CTR modes in TLS, (b) you can implement AES-GCM efficiently in constant time (see http://www.cryptojedi.org/papers/aesbs-20090616.pdf), (c) it is the NSA suite B cipher mode, (d) the alternate mode for AES in TLS (AES-CBC-SHA) requires a new initialization vector for every TLS record, which means that you need to get 128 bits of from your PRNG for every 16KB of data transfered, whereas AES-GCM mode only requires 128 bits total per connection. A strong argument against GCM mode is that OpenSSL, NSS, and the Windows CryptoAPI (prior to Windows 7/2008R2) do not implement it yet.
Do you have a link to something that shows that AES-CTR-HMAC-SHA-256 is really faster than AES-GCM? That is something I've always wondered about.
Since you'll be at a BSD conference, I bet you won't get too many people questioning your suggestion to use OpenSSL. But, in the Linux world it seems there's a big push by Red Hat, SuSe, and other enterprise Linux vendors to replace OpenSSL with NSS in every application they support, because of NSS's huge advantages over OpenSSL w.r.t. FIPS-140 validation.