I'm just annoyed that when Kari and I sat down to watch a movie on the PS3 the other night I had to get my laptop so we could browse movies and find one that was available for instant watch. It didn't dawn on my the 360 did the same thing till last night...it's so much better and a lot less clunky to use.
I have used both fairly often and neither is significantly better than the other from what I can tell. Each has its positives and negatives. The 360's browsing options are limited to about 100 or so of the most recently added items. If you added every single thing available to you via the 360's interface you couldn't fill the Instant Queue. This isn't an issue if you don't have anything specific in mind to watch, but if you want to do something like add all the MST3K or Red Dwarf stuff available you may only find 2-3 in the 360 interface. To add them all you have to go to the Website.
That said, the software on the 360 seems to load faster from the dashboard and is more convenient until the PS3 has it added to the XMB.
On the PS3 side the interface seems to operate more smoothly as it is using what appears to be a BD Live app. Once it is running it runs and connects faster than the one on my 360, likely because it isn't having to run through Xbox Live first, or is somehow tied to the dashboard interface. Similarly, anytime my connection drops to two bars or less on my 360 the 360 just gets stuck giving me a message that my connection is slow and if I continue I will have lag issues. But it never plays. On my PS3, even with one bar, it will always just start playing. If my connection is slow I can pause my PS3 and buffer the video, just like the PC interface. I don't know if the 360 buffers or not because it never gets that far.
And if I want to add or remove movies to my queue on the PS3 I have never had to pull out the laptop because my PS3 has a browser. It can't do the animated menus on Netflix's site, but it can use the search feature.
I primarily use the 360's app just because I don't have to leave my chair, but I switch to the PS3 if my Internet is acting up.. Once it is an XMB app on the PS3 I will see if there are any changes.
And honestly, personally having used Netflix streaming regularly before either console had it, your issue hasn't been one for a long time for me since I have over 200 items in my queue right now and have been watching a lot of TV shows that I don't feel warrant a DVD purchase, like Farscape. And because both interfaces are severely limited to the point that I don't find either of them functional for more than just pushing play I tend to once every week or two spend a break at work sifting through Netflix's site and adding stuff. Clicking "view all" on one genre will bring up multiple pages, each page having nearly as many choices as the whole of the 360's interface.
If you intend to use it regularly you are better off taking some time on a PC to setup your queue in advance and finding all kinds of hidden gems on the site. At that point, assuming you have a steady and strong Internet connection, there is barely a difference between the two.