Most of the time you are in a zone with a monster, and not loading resources, which means it does not affect that much in the hunts.
For example, when playing MHFU, you had an option to preload resources as you are running towards a zone, and also to have most of the game loaded onto the PSP for faster loading. I played with friends that for one reason or another did not do this... all this meant, was that when we were going to a zone, I would always be in the zone a second or 2 before he showed up. This rarely, if ever meant anything meaningful to the overall hunt. I never once said: "If only he zoned in quicker, we could have won."
Is it better to have the new DS over the old one? If you can afford it, go ahead, but it is not game breaking.