Rgb Jpg exports from illustrator never look accurate to what's on screen, but Pdf exports do. Help?

I've had this issue for a number of years with illustrator and still cannot figure out a workaround to get the vibrancy in my logos that I want. My graphics are in rgb, and export with cc profiles, the document is set to rgb, I've tried saving for web, maximum quality and size exports, nothing. Every jpg comes out slightly washed out, but not as bad as pngs. On the other hand, pdfs with profiles embedded have always exported wonderfly for me with full vibrance.

I'm not sure there's a way to export jpgs with the color profile I desire. Or at least, I've tried countless times to do it and haven't succeeded. Is there a way through photoshop or acrobat, to open the pdf version of the file, and revert it to a jpg so that those color profiles stay in tact? I haven't been very successful with it but others may have more ideas than I have.

I will link a side by side comparison between a jpg saved for web with maximum quality, cc profiles on, at 1200 x 1200 resolution, compared to a simple pdf export on the right. I'm not sure if the screenshot will portray it properly but the color difference is obvious in person.