As it's 32-bit application, it can't use more than 2 gb of ram by default. However, if you apply LAA (Large Address Aware) to it, then around 3.2-3.5 gb of ram can be used (from what I remember). So I wouldn't say it's "ram hungry", more like "ram is bottleneck". However if you use DTE materials (which are procedural) instead of bitmaps (image textures), then it's less an issue. Common practice is using image textures for close objects and procedural for medium/faraway distance.

I would say the CPU is important. If I'm not mistaken, Bryce 7 can use up to 8 (physical) cores. So it should render a bit faster there than on quadcore processors. Though there are also different reasons of why/how render time can be longer/quicker depending on your scene (though I guess you may know it already if you worked with Bryce before, stuff like volumetric objects usually increase render time much).