Browsing across Mathematica's website, I noticed they had a "comparison" to MathCAD and other "Calculator Software" (defining MathCAD as "calculator software" is a little demeaning, but anyway...) Here are their claimed advantages over MathCAD (you'll notice most of them are subjective in nature). In short, MathCAD is much more capable than Wolfram would have you believe:
http://www.wolfram.com/products/mathematica/analysis/content/CalculatorSoftware.html
Mathematica.com said:
Key Advantages of Mathematica as Calculator Software:
World's broadest and deepest computational capabilities
I'm not really sure this is a quantitative comparison...
Mathematica.com said:
Automated selection of optimal computational algorithms
Well technically MathCAD does this too, so I'm not sure it's an advantage. Mathematica may have more optimization algorithms available (although they don't explicitly state that).
Mathematica.com said:
State-of-the-art highly automated 2D and 3D visualization
MathCAD does 2-D and 3-D visualization, "state-of-the-art" is pretty subjective...
Mathematica.com said:
High-level solvers for algebraic, differential, recurrence, etc. equations
MathCAD is able to solve all of these problems as well (symbolic or numercial), with built-in functions and solvers.
Mathematica.com said:
Highly consistent interface and syntax for easy learnability and usability
MathCAD is consistent as well, and I would argue easier to learn especially if you have no programming background.
Mathematica.com said:
Rich document-centered interface with embedded live calculations, graphics, etc.
MathCAD also has this.
Mathematica.com said:
Ergonomically optimized free-form mathematical typeset input
I'm not even sure what this means... but I think the gist of what they're getting at is they have "pretty display" equations, which MathCAD does as well.
Mathematica.com said:
Seamless mixing of keyboard or mouse formula entry
If by this they mean you use keyboard and mouse for input, so does MathCAD.
Mathematica.com said:
Real-time error detection during typing
Also available in MathCAD.
Mathematica.com said:
Full publication-quality output
This has more to do with how your format your results and pictures, but there are plently of publications that would accept MathCAD charts and graphs.
Mathematica.com said:
Instant dynamic interface creation
Not sure what this means...
Mathematica.com said:
Web access to thousands of prebuilt calculation interfaces
Plenty of this available with MathCAD too, both in extension packages like the Engineering Packages and online free.
Mathematica.com said:
Free Player for distributing custom calculation interfaces
This I'm not sure MathCAD does, so this is the first real advantage Mathematica has that I see.
Mathematica.com said:
Instant online help with 50,000+ examples
Also available with MathCAD.
Mathematica.com said:
Support for import and export of hundreds of standard and specialized formats
MathCAD imports most data types. I don't know about hundreds but anyway...
Mathematica.com said:
Built-in access to broad external data collections (physics, chemistry, finance, etc.)
Also available in MathCAD.
Mathematica.com said:
Support for international characters, text, Unicode, etc.
Also in MathCAD.
Mathematica.com said:
Fully supported on all standard platforms (Windows, Mac, Linux, ...)
MathCAD is Windows only, so if you're a mac or linux-nerd you'll need an emulator.
Mathematica.com said:
Strong consistent development for two decades
MathCAD has been around for around 15-20 years too I think... not that this is actually a measurement of software quality.
Mathematica.com said:
Web deployment using webMathematica
You can export MathCAD sheets to webpages, but they aren't interactive.