By setting up Storage units and media in NetBackup as hcart, hart3 etc. does not change the way the tapes are read and therefore will not help in increasing the speed that the tapes are written to. These configuration options are only a logical grouping mechanism that NetBackup uses allowing you to group storage units and media. For example, NetBackup will prevent hcart3 media being loaded into a STU of type hcart.
For you to use both LTO3 and LTO4 media in LTO4 drives, you've obviously had to set up all components (LTO3 and LTO4 media and LTO4 drives) as the same type. This allows NetBackup to load an LTO3 tape into an LTO4 drive. Once loaded the physical LTO4 drive make sure that the backwards compatibility kicks in and it will write to the LTO3 media.
Regarding your situation where both the LTO3 and LTO4 media are being written to at the same speed, I would suspect that your bottleneck is elsewhere - possibly network, local disk speeds, Fibre channel. I would try to eliminate these factors first. You can also look around on these forums or the net for some performance tuning settings for your library and drives that might help.
I have the same setup and I get different speeds when duplicating data from local disk SAN to LTO4 and LTO3. I have two dual port HBAs in each media server and I've separated my FC disk traffic from my FC tape traffic.