An LC filter has a steeper slope, because it has two 'active' components rather than just one. Generally you would use RC in an opamp filter, because it's far easier (and cheaper) to obtain resistors than high value inductors, and the opamp makes up for not using inductors. For a passive filter (crossovers etc.) you would usually use LC for the much greater performance.
There is less power dissipated in a LC circuit than an RC circuit. RC is fine for filtering low power signals but when you are trying to filter a high power signal, like RF, LC is better suited.
LC circuits will resonate at a specific frequency.
RLC circuits will resonate over a wider range of frequencies.
RC circuits are small and cheap.
RL circuits are large and expensive. I don’t recall ever encountering one in the field except as a side effect of a transformer.
Nigel, perhaps the term "reactive" would be a better term since "active" is usually used to describe amplifiers, transistors etc.
Certainly for RF you would use LC filters since they give better performance and the inductors and capacitors are small and inexpensive at RF frequencies.