One truth about fishing is you will get as many different answers to questions as there are fishermen. Its up to you to answer for yourself. But to set the record straight about the Accurate 870 2 speed, from this fisherman who has 5 of them and almost only throws jigs, The 870 is a dream to cast. Although mine have the cast control I never use it as I LOVE free spinning reels. I toss jigs from 75 to 200 grams. Both reels you mentioned are wonderful reels but the Avet will not handle the same test lines or give you the same amount of smooth drag as the Boss. Both will handle 40 pound but to me that is where the Avet max's out. Others will tell you the AVet will fish 50# or more but not at the drag settings I use. The boss continues to have perfect free spool and the Avet starts to loose it when fishing 50# or more. The Boss will handle 60# or even 80# though capacity becomes a problem.
I have said this a million times, with the new free spinning reels the angler must use proper casting techniques or they will over spin causing bird's nests.
Those folks who are used to throwing spinners may hate these newer reels as they use a different stroke. For those of us who have thrown conventionals for years we welcome these new super spinning reels and would not consider slowing them down.
Both reels are wonderful for 40#, however the Accurate is my personal choice as the best all around reel for that size.
Best of luck with your new reel