Here's an interesting thought; we can't actually directly compare different forms of transportation because as with all things going high speed you can look at it from 2 frames of reference.
For example, say you have the fastest ship that can be built using known physics, one that is shot off by a huge (length measured in AUs) linear accelerator at 99.[some number of nines]% of the speed of light. Because of time dilation, on-board clocks will measure the trip to Alpha Centauri to take only a matter of seconds, whereas an observer on Earth will see it taking about 4.2 years (actually 8.4 years but hopefully they're smart enough to subtract the 4.2 years it takes for any signal to arrive). So you've got 2 different speeds right there, and how do you compare that to something like an Alcubierre warp drive, with which both clocks would measure roughly the same amount of time, but that time could be, say, a month?
Though to be truthful I'm not actually aware of any fiction that uses the "huge linear mass driver" approach to interstellar travel.
(P.S. Yes obviously one of these ships would not be much good without another matching accelerator at the other end to slow it down again.)