Both databases on the same server? And you are backing up over LAN or the SAN?

Saw this TN:
RMAN backup is slow when AUTOBACKUP CONTROLFILE is configured for the Oracle instance
http://seer.entsupport.symantec.com/docs/305796.htm

Usual performance guides:
Veritas NetBackup (tm) Enterprise Server / Server 6.0 Backup Planning and Performance Tuning Guide for UNIX, Windows, and Linux. This also covers tuning on NetBackup components such as NOM (NetBackup Operations Manager).

NetBackup 6.5 Backup Planning and Performance Tuning Guide (updated October 1, 2008)

RMAN backup is slow when AUTOBACKUP CONTROLFILE is configured for the Oracle instance
http://seer.entsupport.symantec.com/docs/305796.htm

Also check that you dont have a duplex mismatch between the network interface and the switch

What is the throughput for standard backup of this client?

The backup speed is tottally unacceptable in this case.
If it is LAN based backup please check NIC settings on both a client and netbackup server.
It looks like you backup through 100 Mbit Ethernet connection.
You should use dedicated 1Gb NIC on the client to backup such a big Oracle db.
I'd also considered setting up a Gigabit Ethernet trunk  on the client.

@Stuart Green

The other database is on a different server or machine (the one with Kb/s 32108), I'm backing up over LAN.

I found this document regarding NET_BUFFER_SZ http://seer.entsupport.symantec.com/docs/183702.htm

can this one solve the problem?

Additional Info:
I'm using,

Broadcom NetXtreme Gigabit Ethernet

1.0Gbps / LAN

Since the other database server is backing up fast and assuming both are configured the same way, I think the source of problem is likely with the Database server itself.  

Follow the advice of the others and eliminate possible sources one by one.

1.2 TB is huge, so you may also want to consider making this server a media server, so the backup doesn't go over the LAN. 

244Gb in 4hrs is about 17Mb/s, so maybe the performance is not that bad after all.