New Relic's top-down view of the threads in the application shows how much time is devoted to each thread and the methods used inside. The Wall Clock Time is useful for debugging problems with response time for users. An alternative view shows CPU Burn Time, which is useful for diagnosing long computations.
You don't need to use any of these outside features if you want to roll your own dashboard. There's also a generous API that exports most of the basic metrics about your application so that you can integrate this with other tools. Most of the data comes in XML, but there's even a cute little HTML fragment made just for AJAX calls. It's very simple to add website stats to any internal page.
All of these touches will be welcome by some of the more far-flung development teams. If your application is hosted on some distant server and your team works out of a virtual office using Campfire and Twitter to synchronize your workload, then this may be very attractive. If you're a bank that's paranoid about letting anything but heavily scrutinized HTML through your firewall -- well, it's just another reason to worry.
The free version of New Relic is just as much a brochure as the free version of AppDynamics. New Relic offers more thinly sliced pricing plans (Bronze, Silver, Gold, and Enterprise). Upgrading brings better data and longer storage. The free version is good enough if you want to know how fast your machines have been for the last 30 minutes, but it's still a bit too hard to pinpoint the error without some guessing and constant monitoring. The commercial levels offer more and better tools for identifying the errant transactions.
New Relic or AppDynamics? The quality and simplicity of these tools show how much easier it is today to run sophisticated websites at little or no cost. Both of these free tools are excellent mechanisms for tracking the performance of basic websites. They could also be adequate for some larger, more complicated constellations of servers, but the results from big installations will be so complex that any sane person will start paying quickly.
Is one a better deal? If you're running a basic server and you just want to make sure that the database is responding relatively quickly, you can't go wrong with either one. There aren't many potential bottlenecks and both identify them quickly.
There are differences in approach, though, that can tip the scale one way or the other. Before helping Java developers, New Relic began aiming at the world of Ruby developers, who are often consultants working together on projects, often out of virtual offices. Centralizing the data analysis as a service is ideal for groups like this. There's no issue of firewalls. To sweeten the deal, New Relic throws in a number of neat features that Web 2.0 junkies will like.