A bunch of “it depends” here…
The Apple Intel hardware all has SSE3 processors (Intel Core Duo). I hypothetically installed it on an SSE2 processor (Pentium M). So it’s a bit slower, but just like running windows on a Pentium M or Pentium 4 is going to be slower than running Windows on a Core Duo. I guess.
Then there is the matter of software. If the software is a “fat binary” – ie: has both Intel and PPC parts, then it will run really fast, at normal speed. Most new software will be like this – also known as “universal binaries” that run on either IBM or Intel chips and can figure out which one they’re running on, etc.
An example of this is Safari, iTunes, etc. These apps all run at native speed. I’d say just as fast as my iMac G5, but probably a bit slower than a dual-G5.
Then there are the older Mac apps, which are designed to just run on PPC. If you open one of these apps on the intel OS X, they will be run by “Rosetta” – which basically emulates PPC on the fly. These are not going to be as fast as the universal apps, but since these new Intel CPUs are a generation ahead of the PPC ones, perhaps the performance hit isn’t noticable.
Hypothetically, I’ve tried a bunch of stuff on the Dell running OS X, and Microsoft Office 2004, for example, runs at what seemed to be a normal speed. It’s a PPC-only app, which must use Rosetta for emulation.
Then I hypothetically tried Safari and iTunes. Surfing the web with Safari is super fast, much faster than Firefox in Windows on the same machine. Using the PPC version of Firefox is slower than Safari, though, since it has to run through the emulation layer. The “universal” Firefox is due out in March.
Apple has done this before, when they first moved from the 68k chips in the original Macs to the Motorola and IBM PowerPC chips in the '90s. There were apps that could run on either, or they just did the 68k emulation if they weren’t universal apps.