Both spellings are correct, although visionary seems to be least offensive to spellcheckers.
Perhaps the most interesting thing about being visionary, or being a visionery, is that we are taken as a negative, even a frustration to anything useful.
Some definitions:
“given to or characterized by fanciful, not presently workable, or un-practical ideas, views, or schemes: a visionary enthusiast”; “unreal; imaginary; visionary evils”; “Affected by phantoms; disposed to receive impressions on the imagination; given to reverie; apt to receive, and act upon, fancies as if they were realities.”; “Existing in imagination only; not real; fanciful; imaginary; having no solid foundation; as, visionary prospect; a visionary scheme or project.”; “One whose imagination overpowers his reason and controls his judgment; an unpractical schemer; one who builds castles in the air; a daydreamer.”
My favourite is somewhat more positive: “a person of unusually keen foresight.” It is also rather more succinct.
So why the negativity?
Looking at the effect of a 'visionary' on a more mechanistic person, i.e., someone more driven by habit, stayed-culture (e.g., proven or logical), the more cautious or non-adventurer, we see the origins of a particular form of leadership - the visionary leader. Such leaders naturally (and perhaps thankfully) cause issues for the more mechanistic. Although there is no evidence to show mutual exclusivity, it is frequently assumed to great cost.
Visionary leadership theories (which can be termed 'transformational' and may be NLP, Lifecollege, Landmark or otherwise based on future/not past), are all charismatic in some form. Tutors are high to very-high in self-esteem, occasionally bordering on the evangelistic. Learning often involves confidence-building and personal trials – to break past or inhibiting habits.
The learning is at 'events', where a stage is often present and at which it is the the facilitator's ability to tie a follower's self-concept and later self-esteem to the actualization of the leader's goals that comprises the essence of leadership evidenced at events. Transformational learning theories (e.g., Lewis, 2011, Values & Leadership; Lewis, 2012, Further Reaches of Human Nature) support these traditional models of motivation – including Pink's Three (Mastery, Autonomy, Contribution).
It is expected that both students and facilitators enjoy the mutual 'leader – follower' power effects these events generate. Indeed it is frequently the case that it is this effect that is being invested in and which, all being well will create the more confident and successful followers.
It is certainly true that both the tutor and the student can benefit in a transformational way from the experience.
