Jason (one of my players) posted an insightful response here. In which, I either agree with, or at least get where he's coming from.
System Does Matter. That link is an essay from our friend, Ron Edwards, about System. It gets into Narrativist, Gamist, Simulationist, etc. Read it if you're a huge game nerd.
I linked that though, because, well, system does matter. I've been running a Shadowrun of Yesterday game, which is a conversion of Shadowrun to Shadow of Yesterday. Here's the math, for anyone who randomly reads this that isn't a game nerd, and hasn't read back a few pages to see me explain this already. Shadowrun is a near-future, cyberpunk, magic, tech, Usual Suspects and Ronin, dice heavy game. It can be alot of fun. My experience with Shadowrun varies, both from playing and running. Nearly no matter your GM, shadowrun is a game about trying to just fucking live. While trying to get enough karma to initiate, or enough nuyen to get the latest deltaware, or whatever. Like - that's pretty much it for long term motivation in shadowrun. Sure - there's sometimes some "figure out the story-arch mystery" or something. Shadow of Yesterday is totally a narrative game. Its about telling fun and interesting and exciting stories. At least, it is to me. I bet you can already see how these are diverging.
And here's what I'm saying - the game is different. Taking a gamist/simulationist-heavy game like Shadowrun, where your day to day concern is amassing wealth, getting a bigger gun and better armor, and just staying alive, and shoving it into a game like Shadow of Yesterday, where your day to day concerns are Doing Interesting Things and maybe hitting your Keys... well, it creates a different atmosphere. In SroY, you're doing away with the loads of dice from guns, and the shopping lists of gear, and the scraping to try to get that one extra nuyen.
I'm not saying that you can't do a gritty Shadowrun of Yesterday, just that it is not, and can never be the same. Hah. Heck - if you wanted it to be the same, you should still be playing Shadowrun. You could even try a d20 cyberpunk/shadowrun. It'd taste different too.
Death is a pretty heavy motivator in Shadowrun, and its not in SroY. At least, it hasn't been. I suppose that you could tweak the stakes to more closely emulate shadowrun.... maybe that's not such a bad idea. "You win, the two bodyguards are dead. The walls are riddled with bullets, two or three innocent passers-by lie in pools of blood, and the mark stands trembling, untouched. You lose: The bodyguards fired back, and quick. You're bleeding, your companions are bleeding. You are low on ammo and the bodyguards have reinforcements on the way. Its about to get interesting".