Actually, the Eastern slave market was greater, by about 15-20%, than the Western Slave market, with total number estimated to be nearly 15 million slaves shipped in that direction.
Which is not, in and of itself, a surprise. East was dominated, for most of the time of exploitation of Africa, by the Ottoman Empire. That and there was very active Islamic colonization of the Malay area. Additional factors were that to the West majority shipped (about 70%) were men for physical labor (with death rate during transport at 10-12%), while the East consumed mostly women and eunuchs (and survivability in that direction was estimated at less than 50%).
This would also partially explain why the Western slaves' progeny is so numerous today, while in the East it's hardly noticeable and, consequently, produces false impression that East did not engage in slavery except for western colonialism.
In some islamic states slavery was legal up until late 1960s, so I'd say the Western powers would not be the major consumer of slaves in the East.
I will dig up references later - they're a fascinating read, especially since a lot of that info is known for more that a 100 years.
There also has to be something said about the slavery that originated in Europe. Yes, you heard it right: Europe was also source of slaves, which were then shipped to both West and East. There are no definite numbers - there seems to be a lot of information floating around which are dubious at best, but somewhere between 50,00 and one million Irish people were forcibly relocated to the American colonies and forced into indentured servitude. I would, after several researchers, put the number at no more than a 50,000 - 100,000 souls (with the lower number most probable), but it still would be more than 10-25% of the total import of slaves into US (including colonial period).
On the other hand Islamic conquest of and relentless attacks on the West (which would stretch for nearly eleven centuries) may account for similar number of slaves shipped to the Middle East from almost all of Europe as total number extracted from Africa. Again, mostly women and eunuchs, which again would carry very high mortality along the way.
If we add Tartar invasions which would predate Islamic attacks on the Eastern Europe (Russia - Crimea - Poland) the numbers could be even greater...
As to the brutality of the slave trade and the slavery overall it's not as simple as it sounds. Yes, casualties among the slaves, especially in early days, were high. But they were caused by ignorance and generally poor conditions overall. We now know that cramming hundreds of people into wet and hot cargo holds, without adequate food and drink, would inevitably lead to disease and death. Brutality of the slave trade is mostly a myth: after all those people were seen as a commodity and losses were bad for business. Once they arrived to the plantations on the other side of the Atlantic there was somewhat different story, but overall economic considerations were always at the top, and it wasn't only slaves... Mortality among crews of slave ships was at similar levels, if not higher. As a rule crew replacement ratio on - for example - Dutch ships was over 40% YoY. Sex slavery was also a part of that, but it sought mostly mixed-race women and in that case most desired was educated mixed-race woman.
But that's Western direction. Compare that to Eastern direction and you will find completely different story for the most part. Yes, there was a slave labor market part in there, but same considerations apply and we're talking here about overseas dominions of European states, which were not as desperate for manpower. The rest... The rest was, one can safely say, completely different purpose for slaves, and the destination was mostly territories of the islam, with interest in mostly pleasure slavery. And eunuchs. Considering that this market absorbed a lot more slaves (in total, from all sources, including Europe, it could easily be twice that of Western route), the fact that there's very little evidence of it now, among populations of Middle East and Mediterranean, tells volumes about it's brutality.
First of all, in another contrast to West, East procured mostly women. If they were men, then mostly they were castrated after purchase. Just this operation accounted for 50% casualties among male slaves. Skilled slaves - craftsmen, educated men and soldiers - were also sought, but majority of the trade was sexual, so mostly young women and young boys. It was so widespread that it became central policy of almost all islamic states, with Ottoman Empire as most visible example. Indeed, it was banned permanently (because it was banned formally a few times before) just before end of XIX century, and continued as black market for few more decades.
There is a reason that, in stark contrast to Americas, Middle East bears almost no traces of that slavery today. How is possible that descendants of those Americas bound slaves constitute between quarter and a third of the total population? And bear in mind that majority of them were males, so reproduction rates would be initially very low.
Now, there must be raised the point of the treatment of slaves. There is no doubt that slaves in - to use a most basic distinction - Christendom didn't have it great. They were there mostly for manual labor, so neither their welfare nor education nor prosperity were high on the list of their owners. Or lords, in case of indentured servitude incl. serfdom, but this is somewhat special case. For example Polish state(s) relied heavily on serfdom far longer that rest of the civilised world, but even there and then it was far better than slavery in the west and islamic sex slavery wasn't even in the shouting distance.
On the other hand slaves in islam often could attain positions of influence and/or of authority (if latter much rarer, as this is forbidden by the Qur'an), and accepting islam was always the fastest way out of slavery, especially for men. Mamlukes are a prime example of slaves in a position of prestige. In general in Islam slaves were better off than in the west.
But is very curious that slavery in Islam is compared to slavery/serfdom/indentured servitude in Judeo-Christian world, but it explicitly excludes dhimmitude, which was in essence another social level that is usually considered as bottom of a social structure and members treated accordingly. Because if we include that, then there's no comparison, really, between the two.