The DSi browser is a nice feature to get for free, but it falls short of the bar set by the PSP.
The browser is made by Opera, which also has its own computer web browser. The speed is good for the most part. It's not like you're surfing the internet on a desktop, but it's no slouch. The display is nice too, and comes with the ability to alter the view at will. You use the stylus to click links and move around the page, which is done very easily. That's an okay function.
Now, where the browser falls short:
There are no tabs, so you must stay on one site at a time. The memory is too low to open large pages with many things on them such as Facebook or even sometimes the Yahoo home page. That's kind of a letdown, because many great sites won't be displayed to their fullest on the DSi browser. There is also nothing you can really do on the internet other than look. You can't download anything or save images, something the PSP's browser CAN do. So, the DSi browser does indeed fall short of the PSP's. With more memory, many more options, and arguably faster load times, the PSP's browser is superior...and free. So, while this DSi browser is an okay start, we need to see a lot more added to it before it can measure up to the standard we know can be met.