In September of 2013, JAXA launched an $80,\!000\,\mathrm{m^3}$ zero-pressure Helium balloon from Hokkaido[<sup>1</sup>][1]. It reached a float altitude of $53.7\,\mathrm{km}$.

From the ICAO 1993 Standard Atmosphere[<sup>2</sup>][2], the density at that altitude is $6.62\times 10^{-4}\,\mathrm{kg/m^3}$.

That same zero-pressure balloon would float at the same density at Mars. The altitude equivalent to that density will vary over the Martian year, since the mass of the Martian atmosphere varies $\approx\!25\%$ over that time! Since I have MER atmosphere models handy, I find that that density was at an altitude of $\bf 35.7\,\mathrm{\bf km}$, at an L<sub>S</sub> of $328^{\Large\circ}\!$, about two-thirds of the way into Southern Summer (the time of the Spirit landing).

Note that what matters here is density, not pressure. A zero-pressure balloon is an accurate densitometer at float altitude. Also, the difference in the compositions of the atmospheres, in particular the average molar mass, is already accounted for in the density.

[![plot of balloon altitude as a function of time, showing level flight at 53.7 km for 12 minutes][4]][4]

There is one other key difference that could affect the maximum altitude. That is temperature. At float altitude in Earth's atmosphere, the temperature was $264\,\mathrm{K}$. At the equivalent float altitude in Mars' atmosphere, the temperature would be about $178\,\mathrm{K}$. This would have no effect on the float altitude. That is, _if_ the balloon works. However the fact that the Martian atmosphere is much colder than Earth's could change the behavior of the $2.8\,\mathrm{\mu m}$ thin polyethylene envelope. It might become brittle enough that it would not survive launch or ascent, and break when encountering aerodynamic forces, such as gusts of wind. Then the maximum altitude could be _much_ lower, possibly not even making it off the surface of Mars.

By the way, $80,\!000\,\mathrm{m^3}$ may sound like a large balloon, but it's actually pretty small. The mass of the entire system, balloon, helium, gondola, parachute, and payload, was $41.1\,\mathrm{kg}$. Typical scientific high-altitude balloons are measured in the tens of millions of cubic meters, with thousands of kilograms of payload.


  [1]: https://www.researchgate.net/profile/Hideyuki_Fuke/publication/315920020_Recent_Highlights_of_Scientific_Ballooning_in_Japan/links/5bb62c8392851c7fde2e763a/Recent-Highlights-of-Scientific-Ballooning-in-Japan.pdf
  [2]: http://www.aviationchief.com/uploads/9/2/0/9/92098238/icao_doc_7488_-_manual_of_icao_standard_atmosphere_-_3rd_edition_-_1994.pdf
  [4]: https://i.sstatic.net/JhWH4.png