I boil some and steam others! Carrots, I boil because I find they take a long time to cook - although I don't think I have tried steaming them. Zucchini I steam because otherwise it goes really soggy, but if I am in a hurry, I boil as it only takes about 3 minutes to boil up soft, but steaming seems to take 7 or 8 to get the skins softer. I've nto done spinach yet, I've always read that the high iron content can be hard for LOs to digest and my DS has enough trouble digesting ANYTHING so am holding off on spinach for a while. Cauliflower, again it depends on how much time I have - boiling is faster. Peas, I boil. Green beans, I steam.
Generally I find if I want to use it as a finger food, I steam it because it doesn't go as mushy, but if I am going to mush or puree it, then I boil it.
Generally, steaming takes a few minutes longer, but keeps more of the nutrition in. Boiling is faster but the veggie goes mushier.
I bake potatoes, sweet potatoes and squash. For potatoes and sweet pots, I pierce them with a fork a few times and put in the oven until soft. Squash I do like fruits - cut in half, scoop out seeds and bake in a bit of water until soft.
Does that help - not much advice, sorry!