I think you need to also consider what this year has brought us in terms of Disney shutting down. There is talk of Disney opening back up in the middle to end of May, (DIS members particularly) but that could always be pushed back to June 1st. Regardless, if you plan to go the June 2nd option, consider that Disney might not be back to 100% what it usually is. It could take a few weeks to get all their staff back, they might phase-in food location openings, etc. Also, you cannot guarantee what the crowds will be like the beginning of June, as the crowd calendar is partially based on historical data and Disney has never been closed this long. Some fans might rush back the first chance they get, while others might not yet feel comfortable going to a crowded place so soon after the virus eased. (Assuming that is the case.)
I think by October everything should be back to the norm, so it might match your expectations when you think of “typical Disney” and all the connotations associated with that.
Both have their pros and cons, but I wanted to point out some considerations when it came to the June date.