Breloom does still have Fighting as a physical STAB in Emerald, and it has the highest Attack of anything in that game that isn't a legendary, a pseudolegendary, or a Slaking. It would start with Mach Punch at lvl 23, which eliminates Speed issues, and would benefit from TM08 Bulk Up, which you earn with your 2nd gym badge.
For Shiftry, you still need a Leaf Stone. In Emerald, this means you must have beaten Norman (a trainer who is only weak to Fighting, which Breloom supplies outrageously well) since the earliest one is located on Route 119, which can't be reached at first without Surf. Sure, Breloom has weaker Special Attack for its Grass-type moves... but neither one has access to a strong Grass-type move besides Giga Drain (which Breloom can learn by level up as a Shroomish) and Solar Beam, at which point the power gap should stop mattering because you have six gym badges already. In fact, Shiftry and its pre-evolutions can't learn any Grass-type attacks in Pokemon Emerald without TMs, while Breloom has Mega Drain (more reliable than Bullet Seed) when it evolves, and the option of holding out for Giga Drain (stronger than Bullet Seed) later. In order for Shiftry to have its strongest Dark-type attack, Faint Attack, in Emerald, it needs to reach lvl 31 as a Nuzleaf, sporting the same Sp. Atk stat as Breloom. Breloom learns Sky Uppercut at lvl 36, which, at 85 base power and with STAB, utterly humiliates anything Shiftry can hope to do besides Solarbeam.
However, whichever way you decide, it's a good idea to keep a Shroomish in the daycare for the entire game. Spore can only be learnt as a lvl 54 Shroomish, and it is worth every step. Spore + Focus Punch is like an easy button for half of the Elite Four and Battle Frontier. If raising the same Pokemon twice doesn't catch your fancy, go with Shiftry. If balanced stats are an absolute must, Shiftry is probably for you. But if you want a Pokemon that can do one thing extremely well, with the stats and arsenal to back it up, without any fear of its one-dimensional nature, Breloom is the only correct answer.
(Also, in-game, there is little difference between 70 base speed and 80 base speed. At that point, you can just grind until you're faster than things that aren't stupid fast like Swellow and Electrode.)