The cut of the uniform would not necessarily be different -- khaki uniforms of the late 1870s and early 1880s were often produced at the regimental/battalion level, so there was a great deal of variety in terms of detail. A good reference for this sort of thing is the Osprey "British Army on Campaign, 1816-1902, which is a treasure trove for colonial miniatures gamers. It's 4 volumes altogether but volume 3 is devoted to the Crimea.
So for later wars of the 1880s the cut of the jackets is not much of a problem but there is another problem, at least IMHO, which is the leather anklets as opposed to puttees, that they wear on their lower legs. Puttees had become somewhat universal for British troops in the field after the early Sudan campaigns (in which some British infantry simply wore their trousers loose, as most of the Perry Sudan British infantry do).
Still, the Empress figures are quite beautiful and it's not impossible, if you really want to, to convert anklets and lower trousers into puttees, though if you plan on raising a large army it will be very time and labor-intensive. Right now I'm doing a handful of such conversions to some Empress ensigns so they can carry colors for the 66th Infantry at Maiwand. The helmet issue isn't all that tough to solve either, since you can use an X-acto knife and/or sandpaper or a file to smooth out the band around the center of the helmet and create a "covered" version, or use a small amount of model putty to create a pugaree. Of course this takes additional time and effort, before you even get to prime, let alone paint, a figure.
On the size comparison front, Empress, like Perry, are a bit taller than Foundry but close enough for me to accept. Empress side by side with old Ral Partha Zulu War colonials would have the Ral Parthas close to "mini-me" stature.
I should add that for me, the imperfect uniform or equipment issue is not an issue. I try my best to collect figures that are as accurate as possible to my own understanding of what the real troops on campaign looked like at the time but I didn't sweat over fielding my 60th Rifles unit in their Zulu War helmets (without covers or pugarees) when I refought the Second Afghan War battle of Ahmed Khel. Still, if you want one set of British infantry to serve you throughout every theater of the Empire, against Pathans, Zulus, Egyptians, Boers, Mahdists, etc., it's a tough call. It's kind of impossible to get away with khaki uniformed infantry fighting Zulus, at least in public! But if you want to use Empress castings to paint up a variety of British units (some in red, some in khaki) for various Imperial wars in various places against various foes, IMHO you will be fine.
Oh -- and enjoy the wonderful world of late 19th Century colonial gaming!!!