I used Active Sync since I got my very first iPhone, and switched to CardDAV the day Google announced support for it. I can say without a doubt CardDAV is the way to go
With CardDAV, you will get you much more accurate synchronization than with Active Sync. First, as has been mentioned, you can synchronize more than 3 e-mail addresses. In fact, I have 31 e-mail addresses myself, and they finally all sync up with my iPhone. Even more importantly, two-way sync works now. If you make an edit on your iPhone, it won't clobber the field in your Google Contacts. For instance, editing e-mail addresses on your iPhone won't change their labels in Google Contacts to "Other" instead of "Home", "Work", and whatever custom fields you might have had.
In particular, custom fields are preserved in both directions. This is especially important if you want to use Siri to "Send an e-mail to my brother". The "Brother" field in Google Contacts was not correctly imported into iOS through Active Sync, and if you allowed Siri to save who your brother was in your contacts, the import back into Google Contacts mangled everything up, including all other fields that you did not edit.
Finally, phone numbers also all sync in both directions without trouble using CardDAV.
To me, two-way editing (or the lack thereof) was the biggest problem with Active Sync. I never, ever edited any contacts on my iPhone using Active Sync because I didn't want to have to fix all the fields on a desktop later on. Now I can do it freely and haven't noticed any data corruption.
The main gripe people have concerning CardDAV is the lack of push. However, for me Active Sync push was so slow anyway that the slight delay of Fetch barely makes a difference. Plus, my experience with the reliability of Push has been less than stellar (connections that die and are never re-established, primarily). I've found the polling model to be far more robust.
What you may want to avoid while using CardDAV is updating a contact in Gmail or on your iPhone, then immediately updating the same contact in the other. This will likely cause one of your modifications to get overwritten by the modification made in the other direction.
Update: The one oddity I've found in two-way syncing relates to the "Google Voice" phone number type. For some reason it doesn't sync correctly in either direction (it becomes "Phone" on the iPhone when editing in Google Contacts, and "Other" in Google Contacts when edited from the iPhone). My only guess can be that the field has a special meaning to Google.