I've owned two Infinitis, two BMWs and an Audi over the last 15 years and so here are my two cents:
Infinitis are nice cars. They're fast, feature laden and fun to drive. They also maintain relatively good resale value. I personally like their exterior styling and the interior styling greatly improved even between the two Infinitis I had. Also, the suspension on the G35 is tight and corners extremely well, particularly on the larger rim size. They are also relatively inexpensive to maintain (as compared to Bimmers and Audis). Also, dealers are often willing to make a deal on the price (I've scored both of mine at crazy deals, the first one was a new demo, the second was simply new), and the price was the impetus for the purchase in both cases. Both the navigation system and keyless entry/ignition system are amongst the best in the business as well.
The issues I had with them were primarily of the fit and finish variety. Both cars had their fair share of squeaks and rattles. Also, the dealer experience was mediocre at best (but, as I stated earlier, you pay less; but still...). The exhaust note, while nice most of the time, can definitely become an annoying drone, especially on the highway. That same suspension stiffness mentioned earlier means that the ride is harsh and slightly unforgiving over uneven pavement. The material quality in the interior is decent (and improving), but not up to BMW or Audi standards, and shows marks easier.
My experience with Bimmers has shown them to be the best all-around vehicles I have ever owned. I have had a 750il and a 540i and I loved both of these cars. I would have bought another 5 if I didn't dislike the exterior styling of the current one so much. I had the 540, so it was very quick, sounded great and the suspension was easily the most balanced I've ever had on any car - stiffness and feel equal to that of the Infiniti, without the harshness. I test drove a 3-series last year, liked it, but thought it was too small for my needs. I never heard a single squeak or rattle in either of my Bimmers (something I value highly). Also, the materials used in the interior of the car are definitely higher grade than in the Infiniti. My 7 was my favourite car I've ever had, and my 5 was second, to give you an idea of how much I liked them.
The issues I've had with Bimmers is that the dealers are rarely willing to negotiate price (and tend to have an attitude along the lines of "I don't really care if you buy the car, as somebody else will" - which I guess is true, but isn't quite the luxury treatment my girlfriend gets at Lexus). The repair costs once these bad boys come off of warranty can be crippling - in fact, once you get beyond 100,000kms (60,000 miles) I would hesitate to keep them. Brake work is particularly expensive as BMW Service will not just replace pads - they MUST replace rotors too. I've also had a series of lights burn out (exterior and interior) in both cars and had to do radiators on both cars (once each got to be around 5 years old - again, not uncommon with Bimmers). Also, the balance of steering heaviness to lightness was a bit more weighted to heaviness (okay, it was entirely weighted towards heavy) on the 5 series and I wasn't completely a fan of that, particularly in parking lots and parallel parking. My 7 was perfectly heavy on the highway, but light as a feather in parking lots - not sure how BMW pulls that off...
Regarding Audi, I've only had the car a year, but I generally like it. I went with the 3.2 V6, which I'm regretting, but I like the Quattro (it means I can skip the snow tires). The handling isn't quite as tight as either the BMW or the Infiniti, but definitely a more supple ride and I love the exterior and interior style and quality.
In my experience, the comparable BMW is certainly a better, more polished car than the Infiniti - but it comes down to whether you want to pay materially more for that quality, and which exterior (and interior) styling you prefer.