Both options look fantastic; I hope you try them both and keep the one that makes you feel great. I do wonder if the the chocolate brown will feel too dark for June? I'm a person who defaults to dark colours 90% of the time and then regret it when a rare daytime summer event comes up. I bet the dress (I vote green) will accommodate a wider range of toppers if you end up needing one; finding the right length jacket to go over the two-piece may be a bit more finicky.
I agree with you that the dress has an elegant cut and will dress up beautifully with some jewelry and pretty sandals. But then, I've been hanging out in some rather natural-fibre-obsessed online communities, so seeing pretty linen outfits for showers, weddings and other special events doesn't seem at all unusual to me. I think synthetic fibres have somewhat skewed our impression of what constitutes "polished" and created an expectation that clothes never wrinkle, fade, etc. And I bet you anything that if it's warm out there will be plenty of men in slightly rumpled shirts (poplin, madras, all those summer-weight fabrics).