It's likely that you'll have to update your old Airport Express firmware. Next, in case the old AE isn't 802.11
n capable (the current model is), you may have to adjust your network settings accordingly. Finally, if the above adjustments shouldn't help, you may want to experiment with using the old AE to extend the network provided by the new one, rather than the other way around (if I understand your configuration correctly).
By posting back here with the details and results of your changes we may be ably to fine-tune things if and where necessary. Good luck!