I can't remember the title of this story. It was about an expedition in a low-tech spacecraft to a nearby star with a potentially habitable planet. The journey would take several hundred years.
Along the way, each astronaut would wake up from cryogenic sleep from time to time, to perform some duties. One of them wakes up just as the craft is passing an asteroid, takes a few photos, and I vaguely remember him finding out that the man who invented their cryogenic pods... died in one.
The asteroid happens to be a passenger ship going from that system to Earth, or back, pulled out of warp with catastrophic results to avoid crashing with an unknown object (the primitive spacecraft)
In the end, the crew makes it to the planet, find out humans are already there, there's a lush civilization, commerce with Earth, and that humans have become very "posh". They also learn about the plot twist from earlier.