A real time audio analyzer is nothing more than a SPL meter with a certain standard set of frequencies tuned in to show a graphic display of the overall spectrum simultaneously. The 2 units each have specific advantages over the other and are designed to serve 2 different purposes.
The analyzer is mainly used to set an equalizer in a sound system for a desired and repeatable response curve, whether it's flat or tailored to individual preferences. It will take some of the guess work out of setting a system to a predictable tolerance. While a SPL meter can be much more sensitive to room resonances because there is no certain group of frequencies it is tuned to, it can also be very distracting when trying to set an EQ.
The best use of an SPL meter is measuring frequency sweeps for finding problem frequencies and room nodes and dealing with them. Since there are no set frequencies tuned in that the SPL meter works at, you can find very narrow bandwidth response problems that a spectrum analyzer will miss. Some meters have interchangeable microphone heads that alter the pattern of directionality, making them even more useful. But, it's also fun to brag about max SPL!
Most of the Pro Audio type analyzers are set to display 1/3 octave centers all along the audio spectrum, but many are less sensitive and not very effective. If you already have a meter and aren't planning to set the system up a different way or in a different place every few days, just use what you've got and spend that extra money on disks.

Also, remember that in order to get the most accurate results using either type of unit you should place the microphone on a stand, because the proximity of your body will affect the readings.
I hope that helps.