Historically, the Dinobots were big compared to the average Transformer, and even to Optimus Prime.
Optimus, in turn, was larger than most of the other Transformers.
The new Dinobots of Age of Extinction seem to take at least a slight cue from the original Knights of Cybertron of the IDW comic continuity, where they were some of the original Transformers. In the movie continuity, the Knights were charged with protecting the Allspark. I cannot, however, find any reference to them being exceptionally larger than the average Transformer.
Why, exactly, did these new Legendary Knights transform into Dinobots? This was a little cluttered, glossed over and sort of only inferred.
In the opening scene, the "Creator" ships are shown scanning the Earth and sending out Seeds - Cyberforming everything they come across - including Dinosaurs.
Cut to millions of years later. Lockdown is in possession of a ship originally owned/piloted by (some of) the Legendary Knights, where he has (at least some of) them locked up. These Knights are the Dinobots.
There are three somewhat-logical possibilities here (well, as far as any logic goes in the live-action movies).
- During the Cyberforming mission of Earth, dinosaurs were scanned, and those forms given to the Knights, as they were powerful beast forms fitting hugely powerful Transformers.
- We see Earth dinosaurs being Cyberformed. KSI's teams find at least one Cyberformed dinosaur. It is possible that some of the early Cyberformed dinosaurs became at least some of the Knights.
- A mix of the first two: the Knights traveled to Earth during or after the original Cyberforming mission of Earth and found some of the Dinosaurs (Cyberformed, or not) and took on those forms themselves, before somehow being captured by Lockdown later on.