What DSLR to get for a beginner?

I love taking pictures
Right now I have a Canon Powershot sx 40 hs and I love it. But I think it's time to upgrade and I want to try DSLR cameras.

I've had both Nikon and Canon and don't really have a preference. I don't need video so that's not important. I would just like a camera that has the best image quality - with the starter lens (I plan to upgrade to better lenses once I get the hang of it)

I've only looked at the Canon t3i and the Nikon D5100 but can't decide

Is there a camera that has better image quality than those 2?

Also I don't want to spend anything more than $600

Both very good cameras. I'm a Canon user so recommend the Canon. But Nikon users will recommend the Nikon.
You must go into a store and look at both models. Play with them and ask questions, then chose the one that YOU feel happiest with.
Whichever you chose, remember that it will be a brand investment for some years to come.

That depends on what criteria you are using to judge image quality and what the photographs will be used for.

You said "the best image quality - with the starter lens."

Are you talking about sharpness? Saturation? Distortion? Spherochromatism? Different for both at every focal length across every aperture. Which leads into what it will be primarily used for.

It also depends on tons of other factors such as what it will primarily be used for.

If using it largely in lower light photography, Nikon would probably provide better image quality as it has better low light performance.

Good image quality depends heavily on the photographer. There are many ways to overcome various equipment limitations.

Not enough room to write the books needed to answer your question.

Since no additional information is provided, the answer is that if you know what you are doing either one can be used to produce quality images.

Sure if you setup a tripod and capture the same photo with both cameras using the same settings then crop in 100% you can see a discernible difference. If the images are primarily going to be posted on Facebook using 1000 pixels on the longest side, differences in image quality would primarily be perceptible under the strictest scrutiny when placed side by side most likely. Aside from that the differences in features, physical button layout and ergonomics should be a concern in my opinion among battery life and a multitude of other things.

I agree with Photofox. Go into a store and handle both of them and then decide.

Since I had no additional information when I posted this that would be my final word about it.

I was going to give your question a miss because the answers so far cover just about everything I'd advise…

Nowadays there isn't a great deal of difference in image quality between cameras… The entry level models all offer similar quality, you wouldn't be able to tell which shot was taken with any particular camera so image quality isn't what you should be deciding on. Try handling the cameras in store and let your instinct tell you which model feels most comfortable… I use the D5100 with the 18-105 lens, since a lot of kids have now started asking questions about third party battery grips i've thrown a DSTE battery grip on my D5100 for extra battery life (just as an experiment) this gives the camera a bulkier feel and makes it more comfortable for me to handle… This won't be the same for everyone, especially girls who might prefer smaller cameras. You could also throw a battery grip on the Canon, so it's just best if you choose the camera that you feel the most comfortable with, perhaps you'll like the layout of the controls better in one model or you might prefer how the menu system works… Even the weight and the feel of the materials the camera is made of… All these things help influence your decision… So trust your instincts and pick the one that you prefer.

Just a quick edit: I prefer the battery grips that come with 2 trays one for 2 of your camera batteries and one for 6 x AA batteries… Here's the one I use:
http://www.amazon.com/...00BUK4FEG/

Simplicity is a key factor in entry-level DSLRs. They need to keep things easy so that anybody launching into photography for the first time, or upgrading from a compact camera, can get good results without lots of technical knowledge and experience. As such, you can expect fully automatic shooting options and scene modes aplenty, so you can easily tailor camera settings to the picture opportunity at hand.