Saigyo and Dogen were both independent Buddhist monks. Saigyo was, perhaps, even more independent than Dogen in that he seems never to have been strongly identified with one sect, although he clearly did have a great respect for Kukai and, therefore, a leaning toward Shingon. He spent a good deal of time in retreat on Mount Koya, but never actually became a Shingon monk.
Saigyo seems to have kept abreast of current affairs more intently than Dogen did. At least, we have little record that Dogen did so, but, then, the times of Saigyo were more dramatic with major civil war overrunning the country. Dogen may, in fact, have made more effort than Saigyo to curry favour with those who had power and influence, but such efforts were intermittent and brought scant fruit.
Saigyo had seen more of 'the world' than Dogen, in that he had been a samurai and part of the 'north facing guard' of the retired emperor before ordaining. He had clearly had a love life of some kind, but evidence is contradictory and details are lost. Many of his poems reveal him to be a sensitive man who sublimated his passions into a love of beauty. Nonetheless, he also spent much time engaged in rather challenging ascetic practices.
This mix of tenderness and harshness, appreciation of beauty and also of strict discipline, is characteristic of both men. Both came out of an aristocratic tradition, both rejected the worldly life and its hypocrisies, both sought to find an answer to the seemingly contradictory currents of grief and delight that flowed through them as a result of their personal experiences of the Buddhist truth of impermanence. Dogen eventually took his community to the mountains. Saigyo never had a community and went to the mountains alone. Both believed that this kind of yamabushi experience was, as we would say, 'good for the soul'.
Saigyo opened doors for Dogen, especially in the domain of permissible feelings. Where many believed that the proper course for a Buddhist monk was to renounce all passion in a rather self-repressive way, by the time Dogen came along, Saigyo had demonstrated that a Buddhist monk could record his loneliness, grief, longing, sense of desolation, fear of shame, embarassment, sentimentality, and many other emotions and still come to be regarded as a saint.
Saigyo was a follower of the idea of honji suijaku according to which Shinto deities were identified with celestial Buddhas. His sense of religion was, therefore, not at all narrow and could accommodate a wide range of influences, uniting them as much for their aesthetic qualities as for any doctrinal similarities. Dogen is generally portrayed as the founder of a sect, but this designation is rather misleading and, like Saigyo, he united within his approach to Dharma a much wider range of influences than many realise.
Saigyo and Dogen 'spoke the same language' and the wide extension and currency given to this 'language' by Saigyo certainly helped to pave the way for Dogen's masterpieces.