It's so interesting to read all of the differing opinions! We went the last week of June in 2018 and just were there last week (week before easter 2019, April 13-21). June 2018 was awful weather and I'd take last week over it every single time!
The heat, humidity, and so much rain last June was just terrible for us. Every time we wanted to go in the pool in June, it was pouring. We were miserable. We still had a great time, but this past week was so much better.
This past week, the weather was perfect (except fri 4/19 those storms rolled through but after that, everything cooled off). We had our pre-booked fast passes each day, and got more after our first 3. We did have a couple of long fp lines (safari on 4/15 and kali on 4/18), but other than that, no issues. We were even able to get slinky as a fourth fp on 4/17. We don't go on rides without fp so I wasn't paying much attention to standby lines. We went to Epcot for flower and garden booths multiple days and didn't have any lines there either. Maybe we were at mostly the right place at the right time, but would pick this past week over late June for sure!