I can't comment on either (although we looked into those too) but we just got the Kindle Fire HD and it is awesome! You can give DS his own profile. set up parental controls with time limits, etc. It's a lot cheaper than an ipad as well ($189 on Amazon now).
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My mom bought DS the Nabi for Christmas because he loved my Kindle so much. I was not impressed and neither was he. He still uses my Kindle more than I do.
All the features that were supposed to make the Nabi great were annoying to me. The protective case? Falls right off in the hands of a two year old. The free software? Mostly just intro programs requiring you to pay to get the real game. The screen is hard to see from an angle. It kept dropping the wifi connection and wanted my credit card number just to get setup. And the killer? I couldn't download any of the games DS already had on the Kindle. That was our experience.
My sister bought my DD a Nabi a few months ago.. she loves it. It's pretty similar to the iPad since you can get a lot of the same apps. It comes preloaded with a lot of pretty neat games and apps already. The only thing I wish was better is the battery life. It dies after a few hours and then DD throws a tantrum because she doesn't understand she has to wait for it to recharge. Most of the time she just takes daddy's iPad to fill the void.
Re: Nabi vs ipad
All the features that were supposed to make the Nabi great were annoying to me. The protective case? Falls right off in the hands of a two year old. The free software? Mostly just intro programs requiring you to pay to get the real game. The screen is hard to see from an angle. It kept dropping the wifi connection and wanted my credit card number just to get setup. And the killer? I couldn't download any of the games DS already had on the Kindle. That was our experience.