How much, if any, has the new iPad has gained in PDF rendering speed with the A5X processor (quad-core graphics)?
I care a lot about PDFs because as a lawyer I have to review a lot of scanned documents. The performance of PDF rendering on the new iPad depends on the techniques used. For full-resolution rendering, it's a little slower, but software goes a long way. The overall experience depends on four factors:
1) Single-page rendering method 2) Zoom method 3) Caching 4) Pre-rendering
1) Single page rendering: some apps don't display anything until the whole page is rendered. Others render in a tiled fashion: some top to bottom, some in a spiral inside out. Some apps first render a low-res version of the page, then render the full-res version--again, by either of the two methods.
2) Zoom: Again, some apps render on the fly, while others zoom in on the pre-rendered image and pop in the re-rendered tiles or the whole view. The iPad handles vector rescaling (including text) superbly, but rasterized PDFs can't be scaled in real-time if they're in iPad-resolution territory.
3) Caching: some apps don't cache at all, so re-render each time you change the view (even if you're on the same page). Others only cache one page at a time. Still others cache three pages or more, so you can flip pages and zoom in smoothly without re-rendering.
4) Pre-rendering: a few apps will pre-render the next page. One app, described below, pre-renders the whole document.
iBooks and the Amazon Kindle app render large PDFs pretty efficiently. iBooks caches three pages, while Kindle's cache seems to depend on page size. Kindle pre-renders the next page while you're on the preceding page. However, neither support PDF markup. (Kindle also doesn't support rotation
One app, just called "PDF" (by Smalltalk Consulting) pre-renders the entire PDF so that most of the subsequent work is done by the GPU. You set the rendering resolution. The default "2x" gives you around 150dpi, "4x" around 300 dpi, etc. It slows down once you get past 4.5x, but that resolution is sufficient for most applications. This is the best app I've found to scroll quickly through large PDFs. However, it doesn't render markup and doesn't support any markup tools of its own.
In short, the new iPad cannot speed through a 600dpi PDF the way a quad-core i7 with 12GB of RAM can. But it can display and handle large PDF files the way they were meant to be--with the right software.
Goodreader has the best performance of any PDF viewer I've tried, followed by PDF Expert. Certain techniques that worked on the old iPad just don't fly on the new one, so some apps perform very poorly. (Adobe's own Reader is one of these.) Other apps, like iPDF, are promising, but still don't have full Retina support. (Several apps only take advantage of the Retina display when zoomed in, but double the pixels when viewing the whole page.)
To answer the original question and the follow-up: rendering is done by the CPU, display and manipulation (scrolling, zooming) is done by the GPU. The CPU converts the text portions using the text rendering engine and the graphical portions using a bitmap engine. (It's possible that the iPad's text rendering engine is handled by the GPU.)
The CPU on the new iPad is not significantly faster. PDF rendering methods that are CPU-heavy are even slower on the new iPad because the CPU has to do significantly more work to render at the higher resolution. But rendering methods that get data to the GPU quickly perform great. The more rendering work done in the background, the better. A well-designed PDF rendering engine will use idle time to generate image data that's ready for the GPU. An engine that renders "on the fly" (what I called "in real time") will choke.
"Pre-rendering the entire PDF" means that instead of each page being converted to an image as you scroll through, the whole PDF is rendered and loaded into memory as an image. This takes more RAM but results in faster performance when scrolling and zooming. It takes 5-30 seconds (or more) to pre-render the whole file. Also, when zooming in, the image does not re-scale. (Text portions of the PDF won't be crisp if you zoom in.) Google Docs basically does this with PDFs if you want to see what I'm talking about.
Probably little to none - PDFs are rendered in 2D, and most of the benefit of the A5X's graphic processing will be with 3D performance. The A5X is rumored to have twice the RAM of the A5 chip, so that could help with PDF performance if properly utilized. The thing that would help PDF performance the most is a faster CPU or more CPU cores...the A5X CPU is still only dual-core and Apple hasn't announced any improvements in CPU speed. We'll know more about business app performance once the new iPad ships, but for now I wouldn't get your hopes up.
Apparently the new iPad (3rd gen.) can be even slower than the iPad 2 when rendering e.g. PDFs.
The German magazine c't (or rather the new "Mac & i") tested the new iPad (3rd gen.):
Basically apps that need to load and draw more information for the higher resolution may be struggling: The Mac & i app, for example, displays PDFs slower than on the iPad 2, and web pages in Safari sometimes take longer to get rendered. However, this is only apparent in a direct comparison.