It's been a long time since I've used either of these programs and need some advice as to what software would be best for someone to analyze potential circuit designs without building them. Need some good freeware variety.
SPICE is the obvious choice... not sure why you would even consider MATLAB unless there was a specific series of simulations you were running. MATLAB knows nothing of circuits.
Matlab is better at software simulations; sometimes it is easier to make something work in Matlab as a proof of concept before you try to code it in 'C'.
The two programs are almost orthogonal to each other, although, one could, hypothetically, construct a "SPICE"-like simulator in Matlab. But, it would be way slower than SPICE, and you'd spend a lot of calories coding up the diffeq solvers, the node monitors, and graphics displays that SPICE already encompasses.
MATLAB is a general purpose mathematics program, as opposed to SPICE, which is purpose-built.
Depending on what you're actually doing, you might need both programs.
Different tools for different purposes. If Spice has everything you'll ever need, then don't look further. But I would suggest that learning simple state space simulation technique (solve system x' = f(x(t)) where x is a vector of state variables) is a productive endeavor which will put in your toolbox a powerful tool to be used in many different problems beyond circuits. Or to link circuits with non-circuit parts of the system such as thermal or mechanical aspects. In Matlab typically it is the ode45 function.
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I should mention there is a free program "sci-lab" which provides a limited subset of matlab commands. It includes an ordinary differential equation solver (sci-lab "ode" function)
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