There is no need to choose to be depressed. Those two different analytic programs track 2 very different things. They track what they are supposed to track and they should be different if they are tracking properly.
You just need to learn to appreciate the extra data that you have at your disposal, instead of lamenting that you have more (and different) data than you expected.
The server stats show you server stats, which is useful to understand server loads and spider traffic. The browser stats give you browser data and tell you what you need to know about the people visiting your website.
If you are looking to provide credible third party verification of your traffic to advertisers I highly recommend using Quantcast, it is as easy to install as Google analytics, and allows for trusted third party verification of not just visits but actual visitors and demographics of those visitors.