Gameplay wise: No, it doesn't. The disparity is very, very small between the two at higher res.
http://www.tomshardware.com/reviews/fx-4170-core-i3-3220-benchmarks,3314-8.html
Mind you, this is between a fx-4170 and the i3 3220.
If we were to compare a 6300 with the i3, it would look something more similar to this:
http://www.hardwarecanucks.com/foru...15-amd-vishera-fx-6300-fx-4300-review-18.html
"The FX-6300 is the current darling of AMD’s Vishera lineup since it retains a good portion of the FX-8350’s multi threaded performance while allowing purchasers to save over $60. Due to a significantly lower Base Clock, there is still a good amount of daylight between this six-thread variant and more expensive octo-core models so the FX-8350 certainly won’t lose any market share. Intel on the other hand does have something to worry about since the FX-6300 demolishes the similarly priced i3 3225 / 3220 in every test except our gaming benchmarks. Granted, the 32nm architecture used in the FX-6300 isn’t particularly efficient when compared against Intel’s 22nm technology but from a value standpoint, AMD is light years ahead. "
Since his wife would not be caring much about hardcore gaming, the fx would better suit her needs.
Also, although the i3 currently has a better upgrade path, the fx serves better in the interm because I doubt he will take advantage of the upgrade path anytime in the next 5 years if the fx proves snappy enough for him/his wife.
In the end, I believe that the fx processor is the better bang for the buck if he just wanted to do a cheap upgrade for the next few years.
(Even the fx-4300 matches the i3 3220, according to anandtech, also even better in diablo and skyrim!)
(One more edit: If he lives near a microcenter and can take advantage of an amazing sale for an i5, that would be even better.)