Oh, and of course, none of the Nook devices have ads (which you can turn off on any of the Amazon tablets, for $15).
They don't have a model with cellular access (and probably won't) and there aren't a lot of details on their WiFi antennas (Amazon has beefed up this part of their devices, adding two antennas for better reception in areas with low signal, such as remote bedrooms in your house or when sitting outside at Starbucks). Battery and processors on both models are essentially equivalent to what Amazon is claiming in their marketing materials and both companies have included HDMI ports so you can watch on the bigscreen (nice for sharing movies or pictures). Both companies are now claiming unlimited storage for purchased content (which is easy to give you - they don't have to actually store it for each person, but just flag your account for access to a single stored copy).
For Families, both Nook HD models will have individual profile setup out of the box (Amazon has said their FreeTime app for this will ship next month), although it is limited to six profiles (not a problem for most families, but will be for others). There's no info, though, on what either company's choices of settings will be, or if they will be useful for adults to set up a full access profile and one for showing off the device to others (or when visiting the in-laws or using it at church).
Both companies also have built-in apps to sync email, calendars, etc. I'm sure they are great, but I suspect they'll chew up battery life and storage (which I've seen on my Android Tablet, which is always checking for new email). I prefer to keep mine on the web only, which means some features of the built-in browser don't work (well, at least on the Kindle fire - on the older Nook tablet I have, there isn't any type of 'share this page' choice, from what I can tell). You may not be able to install 3rd party apps (from outside the Nook store) on the Nook HD, but they do offer alternate browsers in their store (Dolphin, for example, which isn't in the Amazon store, but which I was able to install as a 3rd party app. One cool feature that I've seen B&N advertising lately is that you can trial Nook apps on your device (Amazon allows trials only on the PC and not for all apps), so you can see if you'll really like it before buying.
Whether or not you want one of the B&N models will come down to where you have the most content, I suspect. With Amazon, I know I can watch movies on my tablet, PC or Roku box, my music is also easily portable. Both lock you in to their platforms for Android Apps (and Google stubbornly refuses to let you set up either one so you can purchase from that store, easily). I haven't tried any of the magazine subscriptions at B&N, but I know that at Amazon, if you cancel a subscription, you lose all your purchased editions, which is why I won't buy much of anything there, other than TV Guide, which is worthless after a week, or single editions (which do stick to your account and can be accessed at any time in the future). A few of my paper subscriptions also have apps that allows me to read on the Kindle Fire; I don't know if they are available on the nook tablets (I haven't looked), but at least a couple were not available thru the Google Play store (at least, not yet).
There are groups already at work trying to root the Kindle Fire HD and will no doubt do the same with the Nook HD tablets, once released (doing this gives you access to the Android store, amongst other things, but sometimes breaks features you get from an un-rooted device) and they may find it easier to set up dual boot with the Nook HD (this has been an option, albeit not one sanctioned by B&N, for the current nook devices, for some time - this gives you the best of both worlds: a completely open tablet or a device tied to their store, so you can use Read In Store).