An ERV improves air quality by diluting the inside air with fresh outside air. The resulting air exchange will remove the concentration of all particulate matter, gasses (CO, CO2, NOx and other fumes from cooking, toxins from cleaners & building materials & electronics, odours, flatulence etc...) and viruses & microorganisms. Further it will pull in natural ozone and oxygen for further air quality improvement.
A HEPA filtration system improves air quality by removing particulate matter from the inside air. HEPA filters require regular filter replacement. Microorganisms are killed by supplemental UV systems. Air exchange is left to imperfections in the building envelope, exhaust fan systems (stove hood, bathroom etc..) and fresh-air intake at the furnace. Air is exchanged while the furnace fan runs, and it can at most be a small fraction of the HVAC system air flow.
Air exchange is thus accomplished with or without an ERV. An ERV does so with better energy efficiency, it can provide moisture control, and it can exchange at a much higher rate than with the furnace's fresh air intake.
A HEPA filter works independent from air exchange, and can improve air quality without heat/cooling energy losses. Moreover, its placement in the HVAC system reduces the recirculation of particulate matter (dust, allergens etc...) and microorganisms from room to room, something an ERV does not prevent directly.
Use the ERV to remove gasses and improve general air quality with fresh outside air. Use a HEPA system with UV to reduce recirculation of pathogens.
To come up with a quantitative conclusion you'd have to quantify many variables, which may be impossible to reliably accomplish. Examples variables are: sources of pathogens, dust, allergens; sources of mold; air circulation patterns; amount of fractional air exchange (furnace fresh air intake, exhaust fans etc...); HEPA maintenance schedule; UV intensity; ERV exchange volume per day; etc...
In critical settings such as hospitals the entire system is controlled and air quality is measured regularly and accurately, and control variables are varied and recorded (yes/no HEPA, UV, ERV volume, occupancy, inside/outside temperature & humidity, energy costs, outside air quality ...).
If you are so inclined, you could have these tests performed as well, but a qualitative answer relying on proven cause and effect may be all most people need. It is true however, that sometimes sophisticated measures are put in place to improve quality or efficiency, but only a fraction of the target is attained due to improper operation & maintenance and/or incorrect assumptions for the situation at hand.