I dont expect AAA titles like Battlefield that push current gen systems to hit NX soon after launch, but if the plattform as a whole is a success EA and co. will bring as much content over as possible.
Nintendo took too long to refresh the Wii with a HD system that could play the hot games PS360 were getting, so i expect them to refresh NX hardware every 2-3 years while offering full BC to previous gens. Especially in this day and age you have to convince publishers that the plattform they are supporting has a future. A whole family of devices having access to the NX content over the next decade is more attractive for EA and Ubi when considering the longterm investment in a plattform. Customers are used to the was Google and Apple their stores and content updates nowadays, so Nintendo better adjust if they wanna reach the kids and young adults growing up with these devices.
I don't think the NX has a very good chance of getting many 3rd party ports of PS4/Xbone games. The rumors are that the hardware's technical capability is similar to the Xbone (maybe a bit more depending on which generation of the Tegra chip ends up being in the final hardware), but going with mobile hardware likely means an added difficulty in porting to the platform.
Taking into account that devs are currently comfortable porting between Xbone/PS4/PC due to the similarity of the platforms, that they'll already have to expand their effort between platforms because of Scropio and Neo, and that the NX will have a much smaller install base than anything else because it's a new platform, I don't think it's ever going to receive many straight up ports of Xbone/PS4 titles.
I think most of its third part support is going to come from the current 3DS/Vita devs (Atlus, Capcom, Spike Chunsoft, Squeenix, Nippon Ichi, Compile Heart/Idea Factory, Koei Tecmo), and if it's able to sell units at a similar pace to the PS4 I can see smaller projects getting greenlit from Ubisoft and EA (Stuff like Grow Home or Unravel). But I don't think its 3rd party library will ever overlap very much with the PS4 or Xbone, especially with western AAA games.