For tastiness, cooking them together is a bad idea.
Most vegetables will be more flavorful if cooked over high, dry heat, as that will get them to brown (chemically altering them, and developing new flavor compounds). If you cook them in liquid with the quinoa, you won't get that.
For vegetables that aren't as great for that type of cooking (eg, brocolli florets), you can throw a little water in the pan and put a lid on it so that you'll steam the insides.
For the nutrition side of things ... well, that's generally considered off topic here, but if cooked together, I would assume that anything that leaches out into the water might be absorbed by the quinoa. But you'd have less risk of over or under cooking if you steamed it separately.
As for it varying by grain ... I probably vary it more by the vegetables:
- I'll dice up carrots and onions and get a little bit of color on them before adding the rice, as I want them to soften up.
- Tomatoes always go in towards the end, as the acidity can keep starches from softening ... but you need to reduce the initial liquid to compensate for the moisture in the tomatoes.
- Summer squashes (yellow squash, zucchini, etc.) are better sauteéd and added at the end.
- Sometimes, you don't want the vegetables to cook, or not cook much. So I'd toss in fresh peas pretty close to when I was going to pull it.