To be honest, the Vita was quite a bit more powerful than the OG 3DS and it came out only months later. The N3DS should have been the OG 3DS in terms of CPU power, and the screen should have been of a higher resolution and bigger, with the corresponding increase in GPU power, and it should of course have had a second stick and the triggers. If the Vita could have the chip it had at that price, so could the 3DS imo.
In a different vein, the Vita could have been like the Switch if Sony had had the courage of doing the Switch's form factor. You take the Vita's chip and give it the power the Switch uses, and you could port PS3 games to it no problem.
Vita came out a full year after the 3DS, not "months". And the N3DS tech simply didn't exist back then (Fun fact, N3DS is the only consumer device ever made with a 4 core ARM 11 CPU! It is also the only consumer device with a face tracking, auto adjusting, auto-stereoscopic screen too!).
3DS was also originally supposed to launch in 2010, not 2011, and all the launch systems were manufactured then. Thus Nintendo were limited to 2010 tech; and the 3DS was very good hardware for that time (CPU choice aside).
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