For me, there is no "distinct cutoff" between what I consider to be modern and vintage. There is a little bit of hard-to-define overlap, and primarily anything that happens to fall within that overlap will be defined either as "modern" or "not modern" depending on my personal interest in that system.
Also, as many others have mentioned, I don't observe just two categories of computer age/generation. Rather, I tend to recognize at least four, maybe five. As of the date I am posting this (January 4th, 2018), my APPROXIMATE cutoffs for these different categories are as follows, in descending order of age:
ANTIQUE: Anything 8-bit and/or made before approx. 1985, but especially anything from the 70s. This is the "maybe fifth" category I alluded to, since large portions of it can also fall into the "Vintage" category below and this could perhaps be better considered a subset of the "Vintage" category, aside from the 70s systems which could make up their own separate "Antique" category.
VINTAGE: Anything in the 80s to approx. 1994, but can also include systems from the "Antique" category above.
RETRO: Anything 1995 to about 2001 or so. Despite being built in 2003, I would personally consider my first ever custom-build as "retro" because at the time it had specs comparable to systems from 2001.
OBSOLETE: Anything 2002-2012. Basically, computers I consider to be old, but not old enough to be of any interest to me unless they have personal significance or importance (Computers I built or bought myself, or spent a lot of time using at work).
MODERN: 2013 and newer. These are systems I'd be comfortable using as a "daily driver" as long as their base specs are good enough for my needs. Depending on how much they've been upgraded, slightly older systems would be acceptable as "Modern" to me.