I think Zen traditions especially seem to emphasize the one distinct moment of enlightenment, but most Theravadins I've talked to have described the journey as a gradual process, albeit one with occasional breakthroughs and jumps.
Gain and loss, status and disgrace,
censure and praise, pleasure and pain:
these conditions among human beings are inconstant,
impermanent, subject to change.
Knowing this, the wise person, mindful,
ponders these changing conditions.
Desirable things don’t charm the mind,
undesirable ones bring no resistance.
His welcoming and rebelling are scattered,
gone to their end,
do not exist.
- Lokavipatti Sutta