It all depends on the goals behind leaving ones star system. If the goal is biological colonization, sending genetic material (or even better a gene database) across large spans of distance and time is far more practical than a generation ship or suspended animation. If the goal is to let your sentient machines explore then you don't even have to be burdened with recreating biological life.
To establish supply lines. If Alpha Centauri has something of value you could send out a self replicating robotic AI entity. It establishes its footing then start sending deliveries to Earth. If each one way trip takes 50 years, after say 120 years you could have a steady supply of resources.
Would Alpha Centauri have resources we lack in our solar system? Mars, Venus, The asteroid belt, various moons and gas giants should be ample for anything we need.
If the robot deposited genetic material over in that system then there would still be genetic material from our solar system in this universe after our sun inevitably explodes, or some unforeseen catastrophe occurs.
We have no evidence that we will ever be able to build sufficiently adaptable systems to engage with unfamiliar environments without constant direct human intervention, which is not possible at light-year (or even light-second) ranges.