Gary Gygax answered this question in an EN World interview, and at more length in Slayer's Guide to Dragons.
Originally there were the five chromatic and evil dragons, each with a color that suited their breath weapon, and a sixth good dragon patterned on the Oriental model of that imaginary creature. As it was both or different origination and alignment I decided to empower the gold dragon so as to more closely resemble the potent Oriental sort. So it got more of everything, including two breath weapons.
There came a time thereafter when more metallic dragons were desirable so as to expand the roster of good, Oriental-type ones. Thus all of them were modeled on the gold dragon template, had two breath weapons.
Logically, with metal value being used as the basis for potency, platunum (Bahamut) being the highest, then gold and silver, the sequence should have been platinum-gold-electrum-silver-copper-bronze. However, I thought bronze looked more potent than copper, and skipped then to brass—that metal conveying some not-so-benign connotations.
See http://rpg.crg4.com/originsD.html#dragon for the longer quote.
Challenge rating
...shows the average level of a party of adventurers for which one creature would make an encounter of moderate difficulty.
This makes challenge rating a better instrument to measure how monsters stack up against a party of adventurers than how monsters stack up against each other.
A more precise instrument to measure how a monster-on-monster battle may run is effective character level (ECL). The Draconomicon lists the lowest-Hit-Dice young red dragon as ECL 19 and the lowest-Hit-Dice young copper dragon as ECL 15. Using these figures (instead of the creatures' challenge ratings or Hit Dice or whatever) makes the aforementioned young copper dragon's encounter with the young red dragon very difficult (DMG 49), which, as you've noted, it is.1
But even this slightly more precise instrument is still a club not a scalpel. Determining which monster wins in an unseen monster-on-monster fight should be the DM's call and used to further the plot, making excuses for the lower-powered monsters when necessary to enhance verisimilitude (e.g. "Yeah, the copper rolled nothing but critical hits and the red failed every saving throw--it was amazing; it's too bad you missed it").
"But what are these creatures' actual CRs?"
Dragons' CRs are far too low if all their strengths are played to--each is, at least, a sorcerer engine in a dragon chassis, after all, and sorcerers are already among the game's most powerful classes--, but dragons are much closer to their printed CR if played like big, meaty melee monsters with the default feats from the Monster Manual (e.g. no Rapidstrike et al., no Shock Trooper, no Travel Devotion). It's the DM's task to make sure that the dragon and the environment in which the dragon's confronted are appropriate to his PCs' abilities instead of either slaughtering the party or allowing a legendary beast be unceremoniously assassinated (unless that's the goal).
A customized-by-the-DM wily young copper dragon that efficiently uses all of its resources can, certainly, defeat a straight-from-the-Monster-Manual young red dragon that's down on its luck, hungry, caught unawares, and used to biting everything to death... but either of those could be an EL 7 encounter. It's part of the DM's job to evaluate each monster to determine its suitability. Encounter design, unfortunately or not, is more art than science.
- That these ECLs are likely excessive is another issue entirely.
Best Answer
Do both of these breaths use the same recharge die? - Yes
Notice how both breath weapons are under the same entry with only one recharge listed. When monsters have attacks or abilities that are separate, they are listed separately. In this case, the dragon's breath weapons are considered one ability with two options. But the ability itself much recharge before it can be used again.
Do you need to roll multiple times for each breath? - No
You only roll one recharge die for the breath weapon ability no matter which breath you use.
Are both breaths expended once one is used? -Kind of
When you use the breath weapon ability you must choose one of the breaths to use. The other isn't expended but you must wait for the ability to recharge before you can choose either again.