I'm not really sure what a "lab scope" is, but a quick Google suggests it's something automotive-related?
Scopemeter: combo oscilloscope and multimeter. Great when you need something to carry around, or you need to take floating measurements (it's not ground-referenced like a bench oscilloscope). Usually a bit of a pain to use and the specs aren't as good for a given price.
Oscilloscope: The real McCoy. High bandwidth, high(er) accuracy, ground-referenced (can be good or bad), easy to use, sophisticated features, simple software interface capabilities, bulky and not portable. Old analog ones don't have as many software features (don't let that make you think they have
none because they're analog, the Tek 24XX series for instance had many), but they make up for that with their ability to double as a deadly weapon if you need to defend yourself.
Graphing multimeter: Very high accuracy and precision (usually the full precision of the meter itself, while most oscilloscopes have 8-bit/256-level precision only). Very slow, only meant to plot long-term trends.