There's no difference. The difference is in an SSD vs HDD for IO speeds, battery life, and weight (thinness). I use a 2009 MacBook with a Core 2 Duo CPU, and it's more than good enough for youtube/facebook/word/etc...
No. Saving a video is related to IO, and if you have an HDD or an SSD, and even where you're saving the video from.
You can easily upgrade the older mac to an SSD, and you wont have any difference is saving videos at all. Now if you're using iMovie or Final Cut Pro to edit videos, you'll notice a big difference in speed between an old and new mac... but otherwise no. If the video is from online, no, there's probably no difference at all as that's internet speed related.
You're thinking of caching while it's compressing something. That isn't worthwhile. I'm not even sure if what you're thinking of is supported by those apps.