Well, the 603's have a just a cardoid pickup pattern. If you dont know what cardoid is, it pretty much means, that the mic pick up things best from the front and the side, and not very well from the back. Kind of like a heart shape, hence the word cardoid.
The 604's have cardoid and have a cap you can put on for an omni pickup pattern. If you don't know what omni is, it means it picks up well all around the mic. Also, the 604 has a -10db pad, nice if you're sound source is loud, and also a low frequency roll off.
They're both great mics, and i'm pretty sure the wires and such inside are the same, mogami wires, which are great. If it were me, I would go for the 604s because I like the extra features. But if you're starting out, maybe you could go for the 603s. There are actually some 603s on ebay that I think have a buy it now price of around 60 or 70 dollars. Not a bad price. If you search around you maybe be able to find them lower as well. It's your choice between the two. Both great mics.