IMO, as someone who lives in NY and doesn't have to contend with extreme heat and humidity, both times are rough in terms of weather. I probably would rather do June because the humidity takes more of a toll on me which seems to be worse in September, and I loathe the daily downpours that seem more common in September. Often the rain can be brief, but we have had total washouts in September before. Its also peak time for hurricane season, whereas June would be towards the beginning of the season and is inclined to be less active. I can't say I've ever seen temps in the 70s and lower 80s in September like PP mentions. We went late October last year and it was still high 80s at that time. IMO, the difference in actual temperature between the two months is negligible.