I believe the artwork for a Podcast is fully dependent upon the Podcaster. It has nothing to do with your Music Library albums, so neither deleting the artwork cache nor Get Album Artwork will solve this.
In addition, the artwork for each Podcast Episode is different to the artwork for the Podcast Series, what you see in your iTunes Library is the Podcast Series artwork. But on the iPod you should see both the Podcast Series artwork (on the Podcast header), and the Podcast Episode artwork when the episode is playing. This can be different and has to be assigned by the Podcast's producer for each episode. They can even set different artwork for different times of within an episode.
So the absence of Series artwork in your iTunes Podcast Library could be because the Podcast's producers have not set any, or they haven't set it correctly. I think this can still be the case even if it's the Series artwork that you can see on your iPod. I guess it depends on which epsiode the iPod is using for the Series artwork.
I have discovered, for example, that one of my Podcasts shows Series Artwork in my iTunes Library,but not on my iPod. So the opposite of your experience.
It also may be that you have only just noticed this since the update to iTunes, which now makes the artwork in the Library more obvious with the new layout.
The "solution" is either to accept things as they are, or to contact each show's producers, asking if they can resolve the situation. They may however, think it's not worth their effort.