RMAN does block level recovery. It is much faster than export. With multiple channel allocation, it can restore 2 TB of database in less than 3 hours(ofcourse its little depends upon your hardware) also
If both databases are on the same server, you could "transfer" the data over DB Links.
If you use normal datapump without DB Links, you'd need to have enough disk space to create the dump files for the data. Also, you'd be doing double the reads and writes (read from source, write to dump, read from dump, write to target) instead of DB Links (read from source, write to target).
Define the DBLink over IPC instead of TCP so that you don't suffer TCP overheads.
for 2TB i think rman clone might be a faster option than expdp/impdp. You will get your data, but index creation and constraint enabling would probably kill you(r timing). No one in their right mind puts production and non-prod on same server, granted there will be some but that would be classic shooting-yourself-in-the-foot.
If you already have a hotbackup, just use it, it will not only make it easier, it will also validate that your backups are actually usable to re-create database which would overwhelm your internal and external auditors with joy.