Below 1000 a bit hard. Xperia tablet z is 1499. Since you want around same size screen as Ipad, it's the only one I would recommend. Btw out of curiosity why change from ios to android? IMO android tablet that can really fight an Ipad not much choice. Don't really recommend going for last year transformer tablets which have high resolution too but using tegra 3. If you don't mind going for smaller size then wait for new nexus 7. Will have FHD resolution and can probably get one within your budget.

Currently in android tablets the nexus 7 probably has the best proc. The S4 pro in it is not like the nexus 4.it uses LPDDR3 and krait 300 cores instead of krait 200 which are found in the nexus 4. Basically in the nexus 7 you get an underclocked S600. If you want better than this then have to wait I guess. Probably nexus 10 or upcoming tegra 4 tablets. Tbh I have no idea why it seems that android tablets don't always get the best proc available or if you're into phablets there's the xperia z ultra. 6.4 inches with s800

I agree with the fact that software matters, its just that tablets seem to be lagging behind when it comes to specs. I mean you would think that being a bigger screen device compared to phones, manufacturers would put high resolutions and better procs in these first. Instead we're seeing 1080p on 4.7 inch screens when 720p is already more than good enough Until now also only a handful of tablets have FHD screens and some have FHD screens with procs that can barely keep up with high reso .