There is negligible difference in taste IMO, though a fully matured portobello has more gill structure than the crimini, which does change the flavor if eaten whole. It's more of a simple matter of personal choice as far as which one you decide to use for any specific purpose. For instance: if you want smaller pieces, and still want people to know for a fact they have mushrooms sitting in front of them, you would probably choose sliced or quartered crimini instead of cubed portobello. You can do things with portobello that you can not do with a crimini. The extra size enables them to be used for other dish elements and variations on texture, and some love to use the gills as another specific ingredient, or one may remove the gill completely (which would be a difficult, tedious task with a crimini) so as to avoid the side effects it may have in a dish.
which would be a difficult, tedious task with a crimini)
I guess that depends on your definition of "difficult" and "tedious." I use the same spoon to scrape the gills, whether the small "baby bellas" or the larger portobella.
The main difference is that I don't always feel the need to remove gills from the smaller ones (they stay tight and closed longer), but almost always scrape them from the larger ones, because they add an off, dirty flavor to the dish.
Point taken, KY. I left out some context I should not have, as I was called away from my keyboard prematurely. What I meant was I never scrape the gills out of a crimini, because when I use criminis, I want the earthy tones they provide. IMO, the young and delicate gills of a crimini are part of what makes a crimini a unique item when compared to buttons and portobellos. If I do not want the muskiness of a crimini, I'll opt for buttons. Of course, there's many things one may do with mushrooms that I do not believe in. A few examples: some of the more elaborate garnish carvings, cleaning with water, or thinking of the stems as a compost material. That is not to say it can't be done, just that I would not as a matter of personal preference and style.
We may already be past the definition stage, but if not:
Portobello are overgrown crimini. Properly speaking, there's no such thing as a baby portobello or any of the other bello diminuitives, only superannuated criminis. Because of the commercial success of portobellos, produce sellers decided to rename criminis. As iplay pointed out, they are the same species (agaricus bisporus) along with buttons.
When the mushrooms are young, white and naive, they're typically called "button." After they age and dry out a little, they darken and the gills start to open. Then they're "crimini" -- the identification is especially easy if they wear they wear a gold chain and an open shirt. As they dry and open further (usually growing quite a bit larger), and get some expensive loafers, they become "portobello."