Cousins is clearly the superior talent. He's elite on offense and at least well above average defensively when he wants to be - which tells me he can be a #1 guy on a contender built the right way. I don't think there are 5 better talents in the league.
Whiteside is a very, very good role player, so it really depends on whether you can utilize him. He's arguably the best rebounding/shotblocking combo in the league, can get you 15+ points on high percentage shots, but also completely lacking in "modern" big man skills of passing and spreading the floor. In a way, he's like Rondo was, able to put up monster stats but also with some negative systemic effects. If you want to win a title with Whiteside, I think you *must* figure out how to run an efficient offense around him, supported by teammates who buy into what he brings.
With either guy, though, the question is whether you can go "all-in". Take either one as your only move, and you could be stuck, or starting over in a couple years.
So to me the question is, can you get one of these guys AND another big piece with some combination of BKN '17, BKN '18, MEM '19, Jaylen Brown, Smart, Rozier, Crowder (if we're bring back a scoring wing), KO, Zizic, Yabusele, etc
It's a lot to ask, but there are scenarios that work on paper.
For example:
Cousins, [Casspi] <=> BKN '16 + Jaylen Brown + MEM '19 + [Amir Johnson, Zeller]
Butler <=> Crowder + BKN '17 + BOS '18 + [KO, Jerebko]
Farrrr fetched, but something down that road makes us a contender overnight. Would use about $15M of our cap room for next year to have both guys instead of Zeller, Brown and Crowder.
Smart/ Bradley/ Butler/ Horford/ Cousins
=> Rozier, Zizic, Yabusele, D Jax, Mickey, vets