Gabriel... at the risk of repeating myself repetitively, redundantly, and repetitively, I don't know of any difference at all between the two.
The 'quality' you're referring to is the speed at which anything past the 'fuck off' frequency of the filter actually fucks off, and you'll see this most often in terms of dB/octave - go farther than said frequency and you'll see less signal surviving. Because of the units we've chosen for our mathematical asshattery, the graph of the attenuation regarded as a function of frequency looks close to a pair of lines joined at an 'elbow' - this 'elbow' holds what we all know as the cutoff frequency, look at such graphs when you have a chance and a few bulbs should start to light. When you get far enough from the elbow, one of the lines will have a noticeable slope - for a lowpass filter you'll have a line with negative slope to the right of the elbow, and for a highpass filter you'll have a line with positive slope to the left of the elbow, and in each case the other side of the elbow will be roughly flat. This slope (or its negative, depending on what you're playing with - absolute value is the important thing anyway, so there's nothing to worry about) is what you'll see referred to as x dB/octave.
The octaves - the distance between a frequency and its double - are typically used. Decades, which are roughly 3.3 octaves (or somewhere thereabouts) are sometimes used - jumping up an octave corresponds to doubling the frequency, while going up a decade is multiplying the frequency by 10 - but you're probably used to seeing octaves. In any case, the two are only a constant multiple away, and thankfully a measurement in decades doesn't mean you'll have to wait several years before the signal changes.
Jeff