I picked up an Asus Infinity a week ago, its a damn nice tablet. And should be getting a Jelly Bean update with in the next few days, if Asus is to be believed.
On the GTab 2 models, they're OMAP4 powered. Laggy with TouchWiz. They are, however, well built and have sd slots. The Note 10.1, yuck. Its thick, heavy, and made of the cheapest plastic imaginable. Despite the Exynos 4412, its also laggy. I was not impressed with the Note 10.1, and neither were pretty much all reviews. Android Police really ripped it a new one.
If you're interested in the forked Android versions from Amazon and B&N, then it might be worth waiting a little longer than a month for the ~9in Fire HD and Nook HD+ to arrive. But, the Fire HD available now though seems to be a mess on the software side.
The Galaxy Note 10.1 is thinner than the ipad and lighter and nobody complains about the weight and size of the iPad. So I dunno where you pulled the information from. It is not laggy and in fact I have used it side by side with the Asus Infinity and the Galaxy was much more snappy. One simple reason, the Asus tablet has very slow I/O speeds so reading off the SD card is very slow. In fact a video loaded on both would literally lag like you were getting fps drops on a slow PC trying to play Crysis.
To me the Note is the better experience even with the smaller screen but the Asus is nicer for reading lots of text. Apparently the Asus also has a few issues with force closing apps and the like. GPS issues, WiFI drop outs etc.
From my perspective the Note 10.1 might not have the fancy new HD screen but it just works plain better out of the box. Also Asus is attempting to block NVflash while you have almost no problem rooting and customizing your experience on the Note 10.1.
Too many people are wowed by the specs of the Asus Infinity and don't do enough research on the various forums to see what people are saying. There's build quality issues and lots of data drops etc. I was considering one but might forget it.
In all honesty if you are not in need of Flash player and you could live without the SD card slot, the Apple Tablets are the best experiences. This is because the OS and all the apps are tailored to the device. The downside is the OS is locked down and you're tied to iTunes.
Should also add that everything changes quickly with new firmware and app updates. Issues I see may never show up when you update.
The one thing that turns me off the asus infinity is the possibility of issues down the line. One video review was comparing it to the note 10.1 and during the review the screen developed two lines running horizontally and nothing fixed it. Restart didn't remove it. Looks like a physical product issue. They said it was 3 months old and was perfectly fine until then but that means dealing with asus support cause retail has 30day return policy. That might be a bad experience.