Use whatever works.
With software capabilities today, there is no empirical reason any one app is better than another.
As long as you pay attention to print specifications - proper bleeds, proper PPI, etc. It really does not matter which app you choose to use. They will all save or export to a PDF/X-1a file which is the standard for offset printing.
Now, application choice can come down to what you are designing.
If your business card is full of photos and glows and "effects", then Photoshop may be a viable choice. It would allow a user to retain all those effects on layers without the hassle of updating linked assets. But you would sacrifice some ease of editing for future cards. That may not be a concern though. (In addition, recent versions of Photoshop offer linking anyway as well as smart objects -- and not all smart objects are vector-based).
If your business card has no photos on it, then Photoshop is generally a poor choice, being raster based. Illustrator or InDesign may be a better option due to the object-oriented nature of the elements and editing. In addition, being vector-based. Indesign and Illustrator will handle things like logos better, assuming the logos are not "photographic".
If you are configuring a lot of cards for a business where names will continually filter in and new cards will constantly be needed, then InDesign may be a better choice. The robust type functionality which exists in InDesign is unmatched in Illustrator or Photoshop, and dealing with constantly changing files is a far more manageable task with InDesign.
If your card is illustrative in nature, then Illustrator may be a better application. The ability to draw intricate artwork or logos as well as transform vector elements (and keep them vector) can be beneficial at times. Updating future cards is not as problematic in Illustrator as it is in Photoshop, but then it may not be as easy as InDesign would be.
InDesign's assent management (linking and master pages) are somewhat irrelevant in my opinion. Photoshop has Smart Objects rather than master pages. Illustrator has Symbols rather than master pages. And both Photoshop and Illustrator will allow you to link to external files so autoupdates occur when those external files change. They all require different set ups, but the same thing is absolutely possible in any of the three applications.
In the end, it's the final press-ready art that is important, not which application you use to get to that art.
It shouldn't be, but if file size (kb) is a concern, InDesign Illustrator and Photoshop will each result in files of different sizes (kb). InDesign will generally be the smallest file size where Photoshop will generally be the largest. But.. for print project, file size really should not be a concern at all. Quality should be.
