The reason you use balanced lines is lower noise and lower distortion, plus the opportunity to eliminate the sonic role that the cable has in the system. BTW, length (or shortness) of the cables has nothing to do with it!
Now if you are using a single-ended source with a balanced amplifier, you will not be able to realize this advantage. Thus comes the idea of a transformer. You would use the transformer directly at the output of the source, keeping the cables between the source and the transformer as short as possible. However the transformer (including the Jensens, which are excellent) will have a sonic artifact which is easily heard, even if properly loaded. If the transformer is kept as close to the source with the cables to it as short as possible, CMRR degradation issues will be minimized.
Now, if the main interconnect cable can be short, you are better off just making the connection with a single-ended cable. The amp, BTW, is not going to give a hoot if it has differential inputs, and the BAT does.
But if the cable is to be very long, over 20 feet, then there will be an advantage to using the transformer solution (assuming an excellent transformer), despite the artifact it introduces, because that artifact will be *less* than that of a single-ended cable being run long distances like that.
Mari555 asks about the other way 'round, where the preamp is balanced and the amp single-ended. There are several ways to do this. The most elegant is to modify the amp with a balanced input, and even though the amp is single-ended, it is possible to set it up so that the amp uses both the non-inverting and the inverting connections of the XLR.
The second method is to use an input transformer that does the conversion.
Finally, an adapter can be used to good effect, and while this technique is cheap and easy- you get what you pay for- it does not take advantage of the balanced output of the preamp and so the resulting sound will not be as good.
Just FWIW, we built the world's first balanced line preamps. We've been answering these questions for a long time.