Personal taste here, but his original was definitely going for a deco/20s-40s vibe. I'd say run with it and go wild.
There is no move away from photoshop -- it's a tool, like a pencil, a compass, or anything else in a designer's box. It'd be like saying "I've noticed painters are using chalk less these days."
The point of Illustrator is to design in vector because your work can be significantly enlarged without visual degradation. It's best for line work and logos. Photoshop is raster (bitmap) and rarely look good bigger than their original size, and it's best for working with photos and photo-realistic stuff.
To answer your question, if your logo design was created in .psd, the only reason you'd need to redo them would be because you didn't design it large enough to begin with, or you plan on employing them for actual use.
Cuteness/cleanness doesn't have any bearing on your choice, and if your work is good nobody will be able to tell which tool you used to create it.