Both would be terrible, but I'd say 3rd party.

Out of those two, going third party seems like the better option to me.

By the way I think this thread should have a third scenario: Nintendo and Google teaming up in gaming. Nintendo would have a bigger audience in mobile (more Android phones sold than iPhones) and the hardware wouldn't be expensive. Nintendo has also worked with Google in the past like that Wii U application that uses Google maps and the Wii Balance board

Nintendo making games for their products could be huge.

Nintendo going 3rd party would be a disaster. Being bought by Apple would be good for them overall. No more worries about sales numbers because the apple crowd would buy their games. They would be floating in cash in a couple years and their franchises are pretty much guaranteed forever.

Going 3rd party would mean to fade into oblivion like Sega and almost every other 3rd party. Gamers won't buy their stuff anyway. At first they claimed it was the hardware. Then they claim its the controller. Nintendo games end up on PS4 and their next excuse would be that they don't buy kiddie games. It would be the ultimate troll and it would destroy Nintendo.

what did apple acquired recently and before?

Nope. I am an Apple-free house, and always will be. I have no intention whatsoever of supporting Apple's business practices, and the Jobsian cult really put me off Apple for life. I'll buy MS hardware before I buy Apple hardware, and I don't buy MS hardware (well except for MS branded keyboards and mouses when they are a better price than the other available brands).

I have never met anyone that loves Nintendo more and hates Apple more than I do. I can't even comprehend them merging. I... 

Easily being bought by Apple, if they went third party they would still be able to make the same quality titles, if they were owned by Apple all their games would be cheap mobile games

Going third party is the worst case scenario since that just means Nintendo's IPs weren't valuable enough to justify a platform in the end. Not only that but it's likely that neither the crowd on the PS4/X1 would be interested in their games anymore so it's also likely that Nintendo's profits will suffer too in the process since they can't sustain their game software business ...

On the other hand Apple acquiring Nintendo could mean a resurgence in the Nintendo brand or something totally different. Apple is smart enough to realize that Nintendo's bread and butter are still dedicated gaming platforms so I doubt they would get Nintendo to focus on iOS or Mac's. With the resources that Apple has it would also be enough to get every third party publisher on board while delivering on an average of 10 AAA console games each year too and more so on handhelds!

Both options could potentially lead to Nintendo shutting down or exiting the videogame market ...