The purpose of analytics is to give you insight as to how your web site (or app) performs with visitors (or users). This insight is really only valuable if you DO something with that collected insight. ie: Optimize your site/process on an ongoing basis.
An important aspect that you left out from your question is: What is your goal for your website?
- Convert visitors to subcribers of your product?
- get visitors to spend more time on your site, thus allowing you to deliver more ads/impressions?
- get more returning visitors
- Sell more of your products in an ecommerce/shopping cart scenario
In each of these scenarios - there may be better software that Google Analytics, but you will want to establish what your primary goal is for using analytics software.
Webtrends, Omniture, and others allow you to monitor social media, video views and other multimedia aspects of a site - and also allow you to integrate them with other platforms (such as email. For example Omniture + an email provider can allow you to send an email to visitors who put 2 or more items into a shopping cart, but then leave without checking out...)
If you just want to see pageviews, and use that as a measuring stick for now - Google Analytics should be fine. You can also use its "goals" features to track when someone fills in a form, or acts in a certain way on your site to determine new measurable metrics to help guide you as you design/redesign your site to benefit your business.
Let us know what sort of scenarios you are dealing with - and what you want your visitors to do more of....the community can then give you a better answer.
Some analytics comparisons i found here: http://webanalytics.globalthoughtz.com/index.php/web-analyti...
One final plug: Marketing Automation (ie: Eloqua, Marketo, Pardot...) software blurs the line between web analytics software and email marketing vendors - it is very useful for creating automated welcome programs, maintaining subscriber status, and capturing form submissions - as well as "closing the loop" on marketing ROI. These are especially useful if your product is anything that has a considered purchase cycle (ie: not an impulse buy)