There are good reasons for using HyperCard and good reasons for using SuperCard. I started using HyperCard, and have in no way reached the limit of its power.
But there are some good reasons for using SuperCard too. SuperCard has in general a much bigger features set than Hypercard. It is easier to make a standard looking Macintosh application in SuperCard.
Colour and Mulitple windowed projects are the two most obvious SuperCard advantages.
As of October 2002 SuperCard 4 which runs in mac OS X is a compelling reason to move to SuperCard.

The future of HyperCard is not looking as good as it could. Apple have not updated it for a while and don't look like doing so.
There was a strong user group campaign to Save HyperCard which you can read about here http://www.hyperactivesw.com/SaveHC.html
There is now a group of users who have exibited at MacWorld to try and whip up interest and support for HyperCard and OS X you can read about that here iHug

The information on these pages might help smooth the transition from HC to SC, for some the best way may be to convert a HC stack to a SC project and fix it up. SuperCard 4 ships with 2 different HyperCard conversion tools.

There is a lot of information on the SuperCard for HyperCard Users pages at SuperCard.us site.

For myself I found making a very simple project from scratch before trying to convert my HyperCard stacks worked.

SuperCard 4 is a lot more friendly to the HyperCard user. Supercard comes with a runtime editor(RTE) whis is live and quite HC like compared to the old Project Editor.

There is also Modulopi an alternate SuperCard 4 RTE from Stéphane Leys. Modular and more powerful that the one that ships with SuperCard. The Beta is free to download.

SuperCard supports many more features than HyperCard.
Some of these are listed below.
Most standard Mac application features are easier to implement with SuperCard. SuperCard supports full color in a native way HC does not.

New October 2002 SC 4 Features Flash 5 Movie Click on the tabs to see all the features. (opens in a new window)

The SuperCard Site gives a comprehensive overview of SC features.

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Some SuperCard Features

Multiple Windows	All SuperCard suports multiple windows in all the major mac os window styles: Dialog, Movable, Palette, Plain, Scrolling, Shadow and Standard.
User Properties	All SuperCard objects can have user defined properties, this is a fantastic feature HyperCard lacks with a myriad of uses.
Vector Graphics	SuperCard has graphic objects in addition to HC' fields and buttons. Tis is another major advantage of SC over HC. SC4 can import and export to all quicktime compatable formats. This makes it very easy to say generate web pages and images from SC
Extended Command and Function Set.	SuperCard has many functions and command beyond supporting most of HyperCard's original ones. Here are a few examples; Functions merge() lineOffset(,[,]) Commands: rotate polygon export pictureData... Features: DragAndDrop, Mac OS Appearance Support, speech recognition And many more... There are a few exceptions SuperCard fields can not share text like HyperCard. SuperCard does not have report printing. or marked cards