You ask a very interesting question. In theory, either network connection should be equally reliable and equally capable of fast file transfers. Other parts of your computer are likely to be more of a bottleneck than the network connections. You do have the advantage of being able to compare the performance of the two network connections using real-world file transfers and comparing the two. I suspect that you will not see a significant difference. However, if one does perform better for you, then go with the one that performs the best.
Are you using Windows or another OS? The Intel® Gigabit CT Desktop Adapter is an entry level server adapter and supports advanced features such as teaming. You mentioned the importance of reliability. If the built-in connection is not a management port, you could pair the two network connections into an Adapter Fault Tolerance team. Then if one connection should fail because of an internal fault, a bad switch port, or a broken cable, the other connection (which will be in standby) can take over. The teaming driver forms a virtual adapter that will add to the overhead of your networking, but I suspect that the additional overhead will not be noticeable on your file transfers. The User Guide and How do I use Teaming with Advanced Networking Services (ANS)? have more information on creating a team.
You might be able to tweak the advanced settings for lower latency or faster transfers. The default settings are settings that work well, and you do not have to change them. However, the settings are available and can affect performance. You can read more at Tuning Intel® Ethernet Adapter throughput performance.
I hope this helps.