There's two main reasons to play DM/SD: 1) Damage - Soul Drain + Against All Odds, and 2) Durability - ToHit Debuff + Defense.
As you already know, the Brute will be tougher simply by virtue of more HP.
Bear in mind, though, that because the Scrapper has higher base damage than the Brute... Soul Drain and Against All Odds will give a bigger increase in damage for a Scrapper. A Brute doesn't benefit as much.
Will the DM/SD Scrapper do more damage than the Brute? Depends on the situation. If the Brute's got both damage buff powers saturated and full Fury...ennh, I suspect it'd do more damage still. I don't know for sure, though; haven't looked at the numbers myself.
But that does assume you're getting the most from your powers and Fury...that ain't always the case. It's hard to keep a full head of Fury on some teams, particularly if there's other brutes (or tanks) grabbing aggro. Or controllers/doms locking stuff down. In that respect the Scrapper has an edge, because your performance is more reliable.
PvP? Ennh. DM/SD isn't that good in PvP. It's not bad, but it ain't great. There's a couple things to consider. Doing negative damage isn't the great advantage it once was, now that resistances are a bit more across-the-board than they used to be.
You're not gonna be getting as much from Soul Drain and Against All Odds in PvP; there just ain't gonna be large clusters of targets for you to buff off.
Finally, for the Brute - it can be quite difficult to sustain Fury in PvP, because folks don't sit still to let you pound on 'em.
@Acyl
VIRTUE
Blue: Realpolitik, Leading Lady, Glass Lass, Superball, Alec Kazam
Red: Battery Acid, Obsolete, Bugfix
How does the two compare in PVE and PVP? I would guess Brutes have greater suvivability but do Scrappers have greater damage overall? Fury + Soul Drain = Win?