when there's an early application cycle definitely take advantage of it since you're competing with fewer people, usually. when its just a regular cycle like after july 5th, i don't think it matters if you submit it by the deadline. but its always good to start early anyway so you don't rush through the application and do everything last minute.
so i suggest starting as early as possible. get organized. take your time. recheck everything. and submit when everything is completed.