What qualifies as old vs new?
The term meme was coined over 40 years ago and describes a concept that dates back through human history so it a pretty broad timeline.

The memes from the 00s count as Old and the memes after 2013-14 count as new?

2010-2012 being a transitional period?

Perhaps.

So All Your Base is way too old, LOLcats would be dead center of Old School, Scumbag Steve and his ilk represent New but stuff like Gangam Style, Doge, and Grumpy Cat are in that middle phase.

And the "dank" memes are the new ones

I’ve gotten mixed messages as to what dank actually means. I’ve seen it used as a category but also an indicator of quality or newness.

I think we can safely include dank for the new memes. All the earlier memes are now called dank because they had a big impact.

I dunno about memes... but my thing about hip-hop is... old school artists had a vocabulary.

Oh they definitely did.

And Kendrick Lamar got a damn Pulitzer. I'm not saying the album wasn't good.. it was way better than most of the other stuff out today, but looking back? Bwahahahaha. Camp Lo "Uptown Saturday Night"? "Illmatic"? Shiiiit... "The Eminem Show". Are you freaking joking? I rest my case.

DAMN was really overhyped. It was great no doubt. But a pulitzer, come on.

New memes > old memes.
Sure old memes have a feeling of being wholesome but new memes are on a whole different level. You can express anything and many people will be able understand and relate no matter the level of degeneracy of the context. This even applies to feelings. You are able to read people based on their level of sensitivity and their preference of memes.
There are memes that talk about beating women, being racist, and causing harm to others, yet many of us bat an eye. In public many will say "stop being racist/sexist/rude" but deep inside we still hold those things.
You see this in every day life where people share memes of suicide and depression. Deep inside many of us feel the urge to kill ourselves but we go against it because we are cowards and have many reasons to continue going, in public you wouldn't even dare to make fun of depression because it's immoral, it is looked down upon. But internet culture is different.

Demotivational Posters were better than any meme.

You can make fun of the ill, the poor, race, sex, and ideologies, and suffer little to no consequence because other people can relate online.
It's such an odd thing that we would not do this in public, speak of such things because they will be looked as weird or act upon our thoughts desire because they are frowned upon. Yet we see these images and consider it "funny" and "relatable".
Memes are weird.

I laugh at most demotivational posters. This one in particular stands out for me... I was in D.C. and it was talking about not smoking K-2 and going with the ganga instead. It was AWESOME.

Those memes with the IMPACT font are all old, no?