Some out there, not myself, say that the teimstream changed after the First Contact movie, and that that change explains some of the "differences" apparent in "Enterprise." I disagree, but it's an interesting idea.
IMHO, having just watched DS9 "Trial and Tribble-ations" last night, I view First Contact the same way. In TOS (2268 or 1968) you see the events play out; after (2372 or 1996) you see some other people in the events but since they don't (negatively) impact the timeline, it's the same events.