The English Wikipedia article on Received Pronunciation uses two particular vowel charts adapted from two sources, an article by Peter Roach titled British English: Received Pronunciation published in the Journal of the International Phonetic Association, and Alan Cruttenden's book titled Gimson's Pronunciation of English. While both sources are reasonably detailed in describing the qualities of /ɜː/ and /ə/ in isolation, as far as I can tell, neither elaborates on quality comparison between these two vowels. The Wikipedia charts are consequently also cursory and just map the two vowels at the same location.
My interpretation is that the quality of these vowels are virtually identical (they have the same tongue gesture and height), with /ɜː/ realized as either a raised [ɜ̝ː], a plain [əː], or a shortened [ə] in unstressed closed syllables. Meanwhile /ə/ could be anything between a plain [ə], a raised [ə̝], a lowered [ə̞], a lower [ɜ], even a really low [ɐ]. /ɜː/ might involve much more tenseness of the tongue than /ə/, but tenseness alone is not exactly audible or perceptible. Length is not that salient either, because in unstressed syllables, especially closed ones, /ɜː/ will naturally be shortened to probably about the same length as /ə/. As you can see, there's simply way too much overlap between these two vowels, that I feel any attempt of figuring out their quality differences is borderline futile.
And in all honesty, in vanishingly scant "minimal pairs," I'm not certain if there's any difference at all. Based on audio evidence from, say, John C. Wells's Longman Pronunciation Dictionary, I can't tell the difference between forward (/ə/) and foreword (/ɜː/). The more I listen to these audio samples, the more I'm convinced that any "phonemic contrast" between /ɜː/ and /ə/ exclusively in unstressed syllables is purely imaginary. I'd even venture that there's simply no point in teaching these two "phonemes" to my ESL students, because I myself, as reasonably competent in the field of phonetics as I'd like to believe, don't know if they truly are phonemes or not, or rather, allophones in free variation in unstressed syllables.
So what would be the most noticeable and understandable phonetic distinction between /ɜː/ and /ə/ in Received Pronunciation?