There are lots of stores nearby in Fort Mill - it has easy access to Rock Hill and South Charlotte. Union County has easy access to south Charlotte mainly the Blakeney and Ballantyne areas. If you're talking about everyday needs - like grocery stores, cleaners, etc., you're going to be closer to what you need in Fort Mill, but there are plenty available in the major residential areas of Union County, too. On these boards, people seem to use "Union County" as a synonym for Marvin/Waxhaw/Weddington. Seems like they're not usually talking about Stallings, Indian Trail and Monroe, which are farther East. The latter tend to be more small town-like, with the former being more like collections of upscale residential developments and some retail and rural areas.
I think there are more stores and services in Fort Mill, but it may just be that I know the area better than I know the Union County areas. And I agree with lovethecarolinas and groove: Fort Mill is MUCH closer to the airport, in terms of drive time. It's also a much faster commute to uptown Charlotte.
Taxes are cheaper in SC, and word is that Union County taxes are going up to cover infrastructure needs. Heaven knows it's needed - phenomenal growth down there in the last 5 years.
What I like about Fort Mill and Tega Cay are that they feel like communities, with community activities and a sense of identity. When I drive through Union County it feels like one subdivision after another. Just my opinion - most of the posters who live in Marvin/Waxhaw/Weddington seem to LOVE their neighborhoods and they find themselves surrounded by other transplants, which makes it easy to make friends.
As with anything, YMMV. Good luck, and enjoy your search! This is one of the fun parts - getting to learn and explore what may be your new home!