Awstats vs Google Analytics

OSE Needed Functions/Does Awstats have them/Does Google Have them

1. Web traffic to any given page at opensourceecology.org and its subdomains?

As far as number of (unique) hits? Both awstats & GA have this feature.

1. Display of traffic history by day, week, month, year time scale?

Yes, as well as hour & day of week. Both awstats & GA have this.

1. Referring keyword that was used to land on a given page?

Yes, both GA & awstats have this.

1. Which website sent a visitor to a given page?

Yes, both GA & awstats have this.

1. Which link or page visitors went to from a page on our website? For example, for tracking that someone clicked on the Eventzilla registration.

No, that's not how HTTP referer headers work https://en.wikipedia.org/wiki/HTTP_referer

1. Support for specific aspects of AdWords that we need to track via Google Analytics?

I have no idea what this is.