Zonal Histogram (QGIS 3.4) has worked successfully for me to derive land cover totals (from a TIF) per county (held as shapefile).
I was searching for an answer to this exact same question. However, a different question (about an equivalent for Zonal Statistics) was where I found this information. To me, Zonal Histogram seems to be a more direct equivalent to Tabulate Area than to Zonal Statistics, so I am posting it here to make the answer more easily searchable.
It calculates a total, not a percentage as per the original question, but it at least makes a percentage possible to calculate.