If I may add to this melange of opinion.
If dragonborn females suckle their young after their born, or hatch or whatever, then they should have boobs. I don't care if they are repitilian, mammalian or whatnot, the only question is "Do they suckle their young?"
If they suckle their young, then boobs are fine and I think it an interesting twist to have such a sauroid looking race be divergent enough to suckle its young.
If the dragonborn female doesn't suckle her young and they hatch, like young dragons, fully capable of tearing the throat out of the closest pey animal offered to them, then boobs are nothing more than a bizarre add on that is serving what is IMO a juvenile aesthetic.
Yes, I did call it juvenile and along with that, its an unsophisticated view of things that would demand that a creature that is so divergent from human (unlike elves, halflings, dwarves or even orcs and goblins) must be portrayed with human secondary sexual characteristics for the sake of "accessibility" or some other such nonsense. RPing gamers are by and large intelligent and hopefully mature enough to accept a more realistic appearing sauroid female creature.
The only gamer I could imagine saying, "That's a girl, where are the boobs?" in regards to a dragonborn are under the age of 14 to be sure. I could easily explain to my 9yr old son the following:
Son: "She's not a girl, she doesn't have boobs."
Me: "Well, you've seen dragons in paintings and in movies and you saw that they, like other creatures that at least appear reptilian like alligators, lizards or dinosaurs, don't have boobs. Dragonborn are related to dragons and don't have boobs either."
Son: "Oh, ok."
That is as complex as the conversation would need to get. If someone above the age of 11 cannot grasp this simple argument, then they have more issues than whether or not dragonborn have boobs.
And honestly, the only argument in favor of boobs on the dragonborn, if they don't suckle their young, is "Its D&D man, it doesn't have to make sense." Of course this is the worst kind of argument because it implies that fantasy equal absurdity when in fact it does not by necessity have to and that the individual making this argument doesn't really have one.
Wyrmshadows