W is on a 16s CD, and costs 30% of her pool at first rank. It leaves her in one tiny-ass area.
Her innate sustain is laughable early on. Sure, it does decently later in the game, but it's in the same boat as Ahri's. Pathetic when it matters, strong when it's all but irrelevant. Gunblade gives her a lot, sure, but it gives anyone a lot of sustain. It's in the nature of the item. You heal for 15% of single-target damage you deal, and 5% of AoE damage. Akali only seems to do better with it than others because most of her damage is single-target.
Her burst is almost entirely backloaded onto the AA proc of her Q. It's that one hit that does so much damage. Sure, her second hit of passive can do a lot, but it's mostly in her Q.
She has poke that having a Specter's Cowl entirely negates, that's how laughable it is. At rank 1, Doran's shield negates it entirely, after your MR is factored in. This is comparable to any toplane champion, who all have some decent poke.
And bruisers aren't meant to beat assassins automatically. Hell, nobody is supposed to autowin against anyone. Not assassins against ADCs, not ADCs against tanks, not tanks against assassins. But that's beside the point. Bruisers and assassins are a very similar class, the only difference being that Bruisers trade in their escape for durability, and some burst for CC (Yes, this means that Rengar is a bruiser, now). Bruisers should no more autowin against assassins than other assassins should. It's a pure skill matchup that's slightly in favor of the bruiser, depending on the assassin in question (Someone like Zed should do worse, since his burst is loaded into his ult, while someone like Akali should do better, because her burst is loaded into a low-CD ability).
Her beating juggernauts is almost certainly because juggernauts almost always build offensively for their first item (almost universally Black Cleaver is rushed, except for pretty much just Nasus, who rushes Iceborn).
Now, if you're still having problems fighting Akali, tell me who you're playing, and I may be able to help you out against her.