Personally I'd tell you to stop trying to cheat aggro matchups and running so much other stupid big shit alongside your giants (i.e. don't run Boom). Handlock generally already beats other control decks by having a built-in cardless draw engine, playing undercosted big dudes and if all else fails converting their hero power to pumping out more severely undercosted big dudes. This also includes playing BGH because fucking hell you already play the most big dudes anyway, and play them the fastest to boot bar godly Druid draws, if you need to kill big dudes then run your shit into theirs. I don't think Emperor does enough either but the Jaraxxus-Inferno thing is really nice. That's three cards. You could also just drop an Argus like many do... I like having both but it is admittedly often clunky.
RE Standard inc: I see absolutely no reason why Savage Roar would be nerfed (or trees). It's an incredibly fair card, the combo is incredibly fair. Grom does 10-12 with an activator, Pyroblast does 10 within a single card... double Fireball is 13 with Hero Power, etc. For the smartass in me, Leeroy + Faceless is 12 from two class-neutral cards. Druid's burst is nothing special at all.
Druid's unfairness stems from their ramp, though I don't see them toning that down any (Innervate is ruined if you drop it to +1 mana, Growth has a very limited T2-T4 window of effective use). The only "problem" is that every successful Druid deck relies on it as a finisher, which itself isn't a problem unless you demand diversity for the sake of diversity. Rather, it's a symptom of Druid's inability to remove big minions. Presumably that's the balancing mechanism behind giving Druids mana ramping, as they're expected to play big dudes first and roll from the tempo advantage but that doesn't work in practice.
It goes something like this: Druid spends entire turn playing big guy. Warrior spend 1 mana to remove it and plays his own big guy to flip the board. Druid spends entire next turn playing big guy but can't remove Warrior's, then Warrior puts him even futher behind and it's GG. Because Druid simply doesn't have viable removal options, Naturalize..., they can't play the long game like Warrior, Priest, Paladin, arguably even Mage can. (Warlock too but Jaraxxus is sort of the ultimate trump card.) The heaviest they get is a high-end "midrange" that ultimately still attempts to mash face to death rather than grind the opponent out of resources.
At any rate, I expect no changes at all. I don't think anything needs to be changed, but just as much I expect Blizzard to bide their time as usual and see what shakes out in the new environment, and next expansion, before making any balance changes to Classic cards.