The Infiniti I30 is the budget luxury car, competing not with full-blooded luxury cars like the Lexus GS300, but more with the likes of upscale cars, including the Buick Le Sabre, Mitsubishi Diamante, and Lexus ES 300. It's Front-Wheel Drive, has a small V-6, and as a result is not a very sporty car to drive. However, for the price, it was a decent car for people who wanted old-fashioned, relaxed luxury like a smooth ride, power everything, and decent gas mileage.
The Lexus GS 300, on the other hand, was a more sporty model with more advanced technology and luxury amenities, competing with the likes of the BMW 5-Series and Mercedes-Benz E-Class. It has the same horsepower as the Infiniti, but adds on a sport-tuned suspension and is able to put the power to the ground better thanks to the Rear-Wheel Drive platform. In my opinion, it also looks better both inside and out.
Gas mileage and reliability are the same in both models, with the gas mileage being in the upper 20s and the reliability being excellent. This means it's all up to your tastes.
Go for the Infiniti if you want a relaxed, upscale car. Go for the Lexus if you're more in line with a sport sedan with luxury features.
I hope this has answered your question. If you have any more, please feel free to ask.