Its unlikely that both types would have been issued (anybody seen primary sources for this?). The army issued only one regimental coat and two of the small clothes. The coats had raw edges and cheap dye. As a result, individual soldiers' coats were brown, orange-y & pink after a season of campaigning. The British Army was very cost-conscious and even charged the troops for their food.
I bought a couple of things before joining my unit and am now the proud owner of a huge knife that is appropriate for the Mexican War.
Yeti, definitely join the unit before buying ANYTHING.