There isn't an exact calculation on how many slaves were brought by each country, or which country these slaves ended up in. However, most research tends to say that Portugal carried more slaves than the British. The estimates are around 5 million enslaved people. Britain was considered the second largest transporter of slaves. These estimates are around 3.1 million. Overall, Britain and Portugal accounted for 70% of the total slave trade.
The primary reason for this was that Britain abolished the slave trade earlier than Portugal. Up until that point, Britain had accounted for the highest rate of transported slaves. Portugal continued the trade nearly 50 years after Britain had abolished it. There were other European countries that contributed, but these two countries had the highest numbers by far.