In the space shooter game Privateer 2: The Darkening, one of the planets, Bex, has a story very similar to your premise; a sublight sleeper colony ship containing religious pilgrims from another inhabited planet was dispatched to the planet on a 500-year journey, but 30 years after they left, superluminal travel was discovered and another ship made the trip in about 3 months, so by the time the original sleeper ship arrived, their planet was fairly highly developed at a level of technology far beyond anything they'd ever seen. The first people to land ended up welcoming the first people to depart, and the planet thus became an interesting juxtaposition of simple agrarian culture on par with Earth's Rennaissance, and high technology far surpassing anything the real Earth has seen.
While not original, yours is still a very interesting question. Some quick math; your original colonists travel 1,170 years at 0.01c. If we simplify this to ignore relativity, periods of acceleration and deceleration, and orbital dynamics requiring elliptical paths even in interstellar space, the new planet orbits a star roughly 11 light-years away. Of that 1000 years, each human is awake for roughly 20% of it with the one awake, 4 asleep rotation, so assuming a normal human lifespan and that the hibernation freezes the person in time in terms of longevity, the last of the original passengers boarding the ship as a very young child would have died about halfway through the journey, and the original colonist's great-grandchildren are the primary working generation aboard.
I agree with your premises that, despite access to the sum total of scientific knowledge as of 2100, the pace of development of anything but pure research would likely be nil, and the first colonists would take a fairly long time to develop the new world to even 2100-era Earth. The nanobots might make things easier as they could be harnessed for mass construction, but technology is inherently iterative. You couldn't put Werner von Braun in a time machine, send him back 1000 years and expect man to have walked on the moon in the 11th Century. The ability for man to walk on the moon developed as a result of all of mankind's other achievements, including sufficient time for those technologies to be applied to the infrastructure of modern civilization. On a new planet, the amount of infrastructure available would be zero; you'd be starting completely from scratch. Orbital dynamics mean very little when you're trying to get your stock of Earth plant life to grow so you have something to eat.
Even worse, a lot of what you think you know wouldn't apply to a new planet; the basic building blocks of life on this new planet might be silicon-based, totally incompatible with carbon-based life, limiting the ability of your new colony to expand organically into the surrounding environment because the ground has to be slowly terraformed by the Earth plants capturing whatever carbon exists and mixing into the soil. Depending on just how different this new planet is, the first colonists might not even be back to the 2100s technologically before the second ship showed up 117 years after the first one made landfall.
The second ship to be launched, travelling at 0.1c, would take just over a century to get to the new world. Let's assume for simplicity that no amount of technological progress has improved the hibernation limitation; colonists on this new ship still spend 1 awake, 4 asleep. When this second ship shows up, its first advantage will be much simpler than you think; a majority of the people aboard the second ship will have walked on the Earth. Assuming we send between 20 and 30-year olds on this second journey, they'll be in their 40s and 50s when they show up, with one grown generation and the beginnings of a third born in space. Contrast this with the math on the first ship; the very oldest arrivals from the first ship would be, at best, the 90-year-old grandchildren of the very youngest of the original passengers, conceived and raised in space. The most productive people from the ship would be great-great and great-great-great grandchildren, for whom the stories of walking on solid ground would be treated with the same wonder and disbelief as our own passed-down tales of our great-grandparents showing up on the family homestead in a covered wagon. At least two generations, possibly 3, of the colonists aboard the first ship will have lived their entire lives in space. When the first settlers got there, even assuming the ship had artificial gravity, the simple idea of walking on a convex surface of solid ground would be a novelty not afforded to the colonists for 3 generations. For many people on the second ship, it'd be a welcome return to what they'd consider normal.
Additional main advantages will be technological; its colonists will have a millenium of additional knowledge the original settlers do not. However, much of that technological advancement will apply to Earth and the Solar System, not necessarily to any ability to colonize this new planet around a new star any faster.
Or maybe it does; humans may have developed their nanotech to the point where they can quickly terraform the new planet with nanobots, or they may bring reentry-capable "terra-bubbles", self-contained domes containing all the essentials and nanotech to build out additional facilities as needed, so they may not need to terraform at all in order to flourish. In addition, if the original colony ship is transmitting data on its progress, then the second colony ship can listen in and gain important technical knowledge discovered by the first colony, which they won't have to re-learn when they get there.
So, all told, I would expect the second colony ship to be in much better shape in almost every way. How they treat the first colonists, and how they are treated, is up to each group. The first group might look at the new arrivals with the same disdain that a lifelong rancher might view the campers in the RV park down the road, whose idea of "roughing it" is driving around in a miniature version of their actual home and who've never had to pull their own food out of the ground or slice it up on the butcher block a single day in their lives. The new arrivals would at first see the original colonists in much the opposite way; primitive, backwards simpletons with no concept of scientific facts they've taken for granted all their lives, like the existence of three more accessible spacial dimensions allowing shortcuts through classical spacetime with no relativistic effects.
