NIKEiD:

-Experience: The first thing I noticed upon entering the site was the layout, very Nike. Good balance of black and colors, clearly has an emphasis on the sleek look of the Nike shoe. Interestingly, I found the use of colors to be almost too great, some of the shoe colors were excessively bright and didn't mesh terribly well the the B&W aesthetic they were aiming for. On the other hand, I am not their target in the least, so perhaps they were right in their choices. The layout on the other hand was cool and intuitive. It was easy to follow the flow of the page from one link to the next.
Clearly the design is SUPER flash intensive, which didn't go over so well on the unusually slow Ithaca network, but once the site was loaded up I had little difficulty. As previously stated, the flow of the site was very strong. Each section led from one to the other, and I found myself inspecting links and finding where they sent me. Eventually this took me to the "What's New" section, and the swiftly to the custom shoe search and design area.
Though this was a nice design for casual viewers I do however, have some questions as to how difficult it would be to use if one were actually trying to accomplish something (like buying a shoe, for instance). There are a massive number of categories, sizes, designs, and several other aspects I was unaware existed till I saw this site. Once again, however, I am not their target. So perhaps the true audience has a better grasp of the inner workings of the shoe industry.
The feel of the site was uniform, and fit well Nike's image. Plenty of pictures of sports stars, mid action, and lots of colorful layouts showing the many different kinds of shoes. The uniform page layout was helpful for one who has no idea where they are going, and at the very least each page was interesting enough that I paged through quite a few before becoming bored.

-Shoe Design:

This here is my beautiful shoe. I believe I may be slightly biased in color choice given the Steelers recent success. Oh well.

Design with Nike was easy, point and click choices, rotating view, a good selection of shoes archetypes. I have a breeze making this shoe, it likely took less than five minutes all together. Honestly any issues I had with it were minor. For starters, the color selection was very limited. Some sections of the shoes had only 4-5 colors to choose from. but that is a minor complaint, that varied depending on the kind of shoe I was trying to make.
Second would be the fact that Nike makes you sign up to save the shoe. This in and of itself was little problem, but their mandatory desire for my home address turned me off from joining. But, as I said, this was a tiny qualm. Aside from those two things I could find no other complains. The layout was efficient, not that flashy, but it is important to be effective before flashy. Controls were super simple and required no thought or knowledge of shoes to employ.
They definitely have Puma beat in this aspect of their site.

Puma Mongolian Shoe BBQ:

Experience:
HA! and I thought NIKEiD was flash heavy, how foolish of me. This crushes Nike in its obligatory use of adobe products.
But, where to start? This site has vastly more purpose than NIKEiD. Unlike Nike the Mongolian Shoe BBQ exists purely to design a shoe from start to finish, and has an easy to follow linear process of doing so. In fact, the entire site experience, from start to finish, is designing your shoe. Once complete you are done, right up to the point where you buy your shoe.
Overall, this leaves quite a bit to be desired as far as "experience" goes. Certainly the site has an amusing aesthetic, and good visuals. The images of the chef, and the restaurant really nail the feel they were going for. If only the flash player on my computer was fully functional I am sure that I would have had a blast for the 5-10 seconds those images went by. But it doesn't, and I didn't. Instead I waited something upwards of 3-5 minutes for each high-res picture to slowly drag by.
So my opinion of the "experience" is certainly colored by my internet connection. I would suggest they add a HTML only version of this site, but it really isn't something that can be accomplished without flash.

Shoe Design:
There it is, my beauty. I called it El Dorado.
Since almost all of this site is shoe design, I assumed that this is where most of the true experience lay. Whether by sheer luck, or superior programming, the connection wasn't nearly as aweful, and thus I actually managed to make this shoe in under 10 minutes.
The first steps in the process were simple. Pick a shoe, pick an existing color scheme (or not), then tweak. It was here that I determined Puma's target to be shoe designers. After all, they are the only people that could possibly need to know all the bloody terms for each part of the shoe that Puma is so kind to provide you with. As a layman I had some difficulty figuring out exactly what I was altering, and was profoundly confused as to why they didn't feel a point-and-click system was a good idea.
Once I got passed all that fluff, the shoe design was rather nice. Different colors and feel from Nike, but with more variety. Here I pondered over texture and color and design. Eventually settling on this black and gold design (for some strange reason I cannot explain).

Comparison:
Each site had their perks. NIKEiD was multi purpose and expansive, while Puma Mongolian Shoe BBQ was narrow and focused. All in all, I'd have to say both succeed where the other fails.
NIKEiD was a good site, certainly. There is a great deal of information to uncover and a massive number of options once you find them. however, in all of this, the custom shoe idea gets lost. It becomes a side note for the many previously existing products. By the end of the process one feels less like they are making their own shoe and more like they are slightly altering and existing brand. Though this may be the case, the thrill of originality is much less.
The community feel of NIKEiD, however, is spot on. Being able to share shoe designs and make wall papers is exactly the sort of thing that keeps users coming back and, eventually, encourages them to buy.
On the flip side Puma's Mongolian Shoe BBQ is the ultimate in style. There is no doubt that (had my computer been fully functional) their site was much cooler and more original than NIKEiD. The greater focus on the shoe design made everything feel much more personal. However, I am afraid their site was too narrow. With little options out side the shoe design, there isn't much there to keep you coming back.
In both cases I found that, by the end of the design, the shoes were so grotesquely expensive that I would never EVER consider using either service as anything more than a time waster. However, when it comes down to it, I would say I would be more likely to use Puma's Mongolian Shoe BBQ. Due to the breadth of options and more direct approach, the actual shoe design portion of the site is superior to that of NIKEiD. But as a marketing tool for spreading their product NIKEiD is by far the superior site.