In liquid cultures with inorganic ferrous sulfate At. ferrooxidans and L. ferrooxidans grow fine but when trying to isolate on solid medium which is growing successfully At. ferrooxidans and L. ferrooxidans show no reproducible sporadic growth.
Leptospirillum spp. are even more sensitive to organic C byproducts than At. ferrooxidans. Leptospirillum spp. also have usually a lower optimum pH and tolerates extreme low pH with some species being found in the Iron Mountain at pH close to 0 or even lower. And Leptospirillum spp. aren't inhibited by a high Fe(III)/Fe(II) ratio or redox potential, conditions in where At. ferrooxidans cannot obtain energy...
That's in general the differences in growth. Respect the solid medium, many Leptospirillum spp. were not succesfully incubated in plates, not even using overlay culturing techniques. The technique consists in plates with 2 layers of 2 different culture media, being the bottom inoculated with a heterotrophic acidophile, generally Acidophilium, which will consume the residual free carbohydrates from the agar and the produced organic carbon byproducts generated by the chemolithoautotroph cultured on the top layer.
This is why all the biomining is quite biased towards Acidithiobacillus ferrooxidans, as it was the only easily culturable acidophilic iron oxidizer for nearly 50 years, even knowing nowadays that in many cases Leptospirillum spp. completely overrules Acidithiobacillus ferrooxidans and in some cases the later is barely present.
The growth temperature of the two strains may be different, rather than the problem of culture medium. In addition, agar in the culture medium may hydrolyze to form an organic environment and inhibit the growth of the two bacteria.