Mathcad Prime vs Matlab

Mathcad Prime is being developed as a replacement for the "original" versions of Mathcad (the last one was Mathcad 15,) and has a far amount of work required to get up to that level.

Matlab is a fully mature program with a large embedded base of applications.

Let's see:

• Programming?  Matlab is a programming language.  Mathcad is not primarily a user code engine--you can write a program in Mathcad but many sheets do not require it.  Think of Mathcad more as a piece of paper--you write your equations out (they look very similar to what you would create with a pencil) and the paper takes care of the arithmetic. 
• setting equations?  Mathcad is easier for a non-programmer to read and understand.  WYSIWYG!
• algorithms?  I'm not sure what you mean.  Mathcad looks like you wrote it down, Matlab looks like computer code.
• Displaying charts?  There have always been complaints about Mathcad's graphing, Prime is worse than 15 is, and promised improvements have been delayed and delayed.  Matlab is capable of producing seperate graphic files with graphs arranged and grouped on a single page. Mathcad, you copy a bit map. ( Pie charts?   ROFL!) 

Take a look at Smath studio: Smath and Octave: Octave. Both are free. Smath has a whiteboard interfrace like Mathcad, and a very similar syntax. It can't read or save mathcad files though. Octave is a free Matlab clone. It can read and run many Matlab files, but not all of them. It does not have all the bells and whistles of Matlab, but what do you exptect for the grand cost of $0? . You can play around with them, at no cost, and get an idea of the difference.

Something that you might want to consider is that starting next year PTC is going to a subscription only model. So you could buy Prime 4 now (and thereby get Mathcad 15 for free) with a perpetual license, but you will not be able to buy any upgrade with a perpetual license.