There is nothing wrong with crystal based radios. That's what I've had since 2001 and I plan to use it as long as I can.
For the Futaba, read the info at
http://www.futaba-rc.com/faq/service-faq.html#q41 to determine if it is legal to use in the US. Futaba 5 channel transmitters have been out of production for a long time.
Similar info may be available for the Airtronics at
http://www.airtronics.net and if not there should be a phone number so you can check on it.
If the battery packs are bad you may or may not want to spend any money to replace. You can get packs from
http://www.hangtimes.com/txpacks.html and other sources but the prices are pretty high (more than $30) to revive old equipment.
If you do decide to get a new transmiiter and receiver(s), your servos may or may not plug into the receiver without modification. Extremely old Futaba servos had what they called a 'G' connector. Some of the pins were exposed rather than being hidden inside a plastic housing. The connectors can be replaced by cutting the wires and soldering these
http://www.servocity.com/html/male_servo_leads.html on. Old Airtronics servos had the wires in the connectors differently than every other brand. On them, the pins can be removed from the connector and reinserted in theright locations for modern receivers.