Image looks fine in Illustrator but is low quality and pixelated when exported

[Sumi235808482h9i]

Hi all, I'm working with this display ad and it looks fine within Illustrator but no matter what I do when exporting it looks come very pixelated (screenshots attached). My document is at 72ppi and the ad size is 300x600. I've tried Save for Web and Export As and neither makes much of a difference. I haven't had this issue with previous ad designs so I'm wondering what's going on 

[Monika Gause]

At 300 x 600 pixels that's all you can expect. There's just too much detail going on.

[Ton Frederiks]

Sometimes it can be improved a little by using the Art Optimized Anti-aliasing option.