Oscilloscope with FFT or a Spectrum Analyzer?
To answer simply - an oscilloscope is an essential tool for any electronics lab, whilst an SA is generally not (unless you are an RF engineer, and even then you need a good scope) and for a good quality one much more expensive in comparison (though Rigol have just brought out some pretty powerful SAs at decent scope type prices)
The FFT function on your average DSO will do for most work, so unless your frequency range of interest is e.g. > 500MHz or so (if it is let us know), then the DSO is the tool of choice. 

Basically one does amplitude versus time (scope), and the other does amplitude versus frequency (SA)  

Scope example:
Say you have a digital signal that is intermittently working, you could check on the scope and look for over/undershoot, ringing, noise, gltiches, etc.  



(simple) SA example:
Say you have a signal and you want to check the harmonic components of it, you can look on the SA screen and check for harmonics (e.g. a pure sine wave should just be one single spike on the screen, at it's frequency, a square wave would be a decreasing series of odd harmonics)  

Square wave on a Spectrum Analyser: 



The same signal on a scope would look like this: