What is the difference between ISO/IEC 14443 and ISO 7816 smart cards
The original answer is correct, but it lacks details.

ISO14443 is a contactless protocol (cards with an antenna embedded). It specifies only the lower-level of the communication protocol (what happens on the physical / link layer), but it does not specify the commands available at the upper level.

ISO7816 is a specification that was initially written for contact-only cards (cards with the pins exposed in the plastic). It is split in different parts:


Parts 1 to 3 are the description of the physical / link layer part of the protocol
Part 4 (and above) describe the standardized commands on the upper layer


So usually, contactless cards comply with ISO14443, and optionally with ISO7816 part 4. But when you talk about ISO7816 compliant cards without saying more, you usually refer to contact-only cards (you can also find cards that have dual interface).

So, to sum up, the huge difference between Mifare and Parallax IS23SC4442 is that the former is a contactless cards (that don't even have a contact interface) and the latter is contact-only. Then, choosing between one or the other is easy: it depends on your application. Do you need contactless or contact cards ?