I have driven two similar cars that am considering: the 07 G35 Sport versus the IS350. I also tried the G35X.
The biggest difference between the cars you are looking at, IMO, is the engine. The G has a lot of power, but will also get much worse fuel economy, especially if you use the extra power frequently. My opinion of the IS250 is that it needs about 30 more HP. By today's standards, the IS250 AWD is dog slow. But if the IS250 has enough power for you, then you might as well save the gas.
On the luxury side, I feel that Lexus is overrated. The green digital clock and silver plastic center console don't exactly scream "luxury" to me; the styling reminds me more of a $20 Wal-Mart clock radio. In terms of electronic features, you can easily get a number of options for the G that either aren't available at all (real time traffic display, integrated hard drive) or can be hard to find (name-brand audio, adaptive cruise control) on the IS. Also, the configuration of the auxilliary audio/video inputs and the 12V power socket in the arm rest are much more useful in the G than the IS. On the other hand, I would trust the Lexus build quality more than Infiniti's, and the Lexus has a quieter and smoother ride. It also has a few exclusive bells and whistles of its own such as ventilated seats and rain-sensing wipers. The Lexus controls are simple and generally intuitive; the G35 on the other hand goes for a busy arrangement of knobs and buttons.
In terms of driving feel, I found that the G drives like a large car, whereas the Lexus feels smaller and more maneuverable. The G35X felt softer than I expected; I liked the Sport more. The G gets its handling prowess the old fashioned way: a good, hard suspension. The Lexus has a more European feel, with a more compliant ride that is still offers very good control.
The size difference is more than slight. If I recall, the G is 7 inches longer. In car terms, that's a lot. If I recall, the IS is technically a sub-compact and the G is a midsize sedan. The G has a much more useful back seat. The Lexus suffers from a puzzling packaging problem; it's actually 2 inches longer than my old 99 Audi A4 and yet officially has less rear leg room and a smaller trunk. Its back seat is one of the nicest, most luxurious torture chambers that you'll ever see. Unfortunately, neither car's back seat folds.
This is a tough choice. By many criteria, the G is both sportier and more practical, but Lexus has some intangible benefits that are hard to ignore. I'm still on the fence and hope more people will chime in.