Flower initiation begins in summer - if the ground is dry, then the process either doesn't start, or aborts, so if your large Camellia might have gone short of water at that time, that could explain it. Presumably, as its the large Camellia with the problem, it doesn't receive early morning sun in winter - early sun on buds covered in frost can cause all the buds to fall off. Those are the two usual causes of no flowers, if the plant is otherwise entirely healthy.

Also, if the large one got a heavy pruning in summer, that might prevent bud formation.