I've used many different rack setups over the years from Tama, Gibraltar, and Pearl. Playing a minimum of 2 shows a week (usually more), the rack, while providing a smaller footprint (though not much if you position your stands creatively), was more of a hassle than it was worth.
First off, for it to be quicker to set up and tear down, you need to leave all cymbal and tom arms attached, and just separate the vertical rack bars from the horizontal rack bars. Now you have three big, long, heavy, awkward pieces of metal (with all the arms coming off of them at various angles) that won't fit into any regular hardware case. Next, you have the issue of the rigidity of the rack. Yeah, it's nice and stable IF the floor/stage/riser is level and even. However, if you're playing on some janky stage that flexes when you walk on it (as some smaller venues tend to have), or you're forced to set up on a multi-piece stage or riser and end up on an uneven seam, your rack will undoubtedly wobble, and you'll have to adjust the legs to accommodate, eating up any time you MAY have saved by using it instead of stands.
Depending on the size of your kit, stands will most likely be a better option in terms of transporting, weight, and set-up/tear-down. For reference, I've included a picture of my kit. Aside from my snare and hihat stands (which you would most likely be using with a rack too), I've got 3 toms and five cymbals all mounted on two stands, and I could probably fit more if I wanted to. To pack up, I remove the cymbal booms (just the booms, I leave all the vertical tubes in place), fold the tripods, and stick everything in an SKB rolling golf club case (usually cheaper than their dedicated drum hardware cases).
However, if you have a drum tech to set it up and tear it down for you, go nuts, man. haha