The performance benefit of a 1GB DRAM in any individual benchmark is negligible. In fact, normal smartphone usage (even with multitasking) doesn't require more than 512MB of system memory at this point. You can get close, but it's pretty challenging to go over given the requirements of Android 2.2.1 and popular apps today. As a result you won't see the 1GB of memory give Motorola an edge in any benchmarks.
Despite the extra DRAM, Motorola is actually at a disadvantage in many benchmarks. The motoBlur UI enhancements and skinning do impact performance. Even after using a task killer to stop all non-system processes, some components of motoBlur will automatically restart. Thankfully two Cortex A9s are enough to hide this from being a problem in the day to day usage of the phone, but it does mean that the Atrix 4G sometimes benchmarks slightly lower than the Optimus 2X.
After using the Atrix 4G as my only smartphone I must say, I completely agree with Brian's assessment. The dual Cortex A9s in NVIDIA's Tegra 2 make Android so much better. Even though the Atrix 4G is only running Froyo (2.2.1) it felt like the fastest Android phone I'd ever used, including my brief stint with the Nexus S.
You see the Nexus S's partially GPU accelerated build of Android (Gingerbread) makes scrolling through your list of apps buttery smooth. Even the Atrix 4G lacks that. Every now and then you get a stutter or hiccup, but it's usually pretty good.
Where the Nexus S falls short however is in actual application response time and in performance when switching between apps. Trips back to the home screen, launching new apps and even interacting with apps all feels quicker on the Atrix 4G than anything sans-Tegra 2.