Bar Cart vs. Bar Cabinet - You Decide
I LOVE a bar cart - the mobility of it. The jewel-like quality of it. And if you've ever been to the barn, you've seen how much I style with beautiful liquor bottles. To me, the bar cart gives a sense of spontaneity and effortless entertaining.
On the other hand, the bar cabinet can be contained in a period secretary - closed and discreet most of the time, but upon opening it, you're treated to a pull-out bar counter, and accessible libations and glassware.
And that does bring a down-side to the bar cart: if you live in a dusty area, your glassware can suffer from being out and exposed. (Although that can be countered by leaving them upside down, or simply keeping the glasses themselves in a nearby, convenient cabinet.

There's also the humble bar tray, which I have in my kitchen (where fresh ice is always at the ready!). So there are many answers to this question.
House Beautiful's Lauren Taylor was pondering the same issue, and polled 10 interior designers for their take on the subject. Here's what she learned:
"If you don’t have space at home for a built-in bar but you want a dedicated cocktail-making area, you have two options: getting a bar cabinet or a bar cart. Both do the same thing—they hold liquor bottles, glassware, and other bar accessories—though each brings a different vibe and overall look to an interior.
The Case for the Bar Cabinet
While most designers can appreciate a good bar cart, there’s a certain level of elegance and sophistication that comes from a bar cabinet.
“There’s something alluring about opening a cabinet and discovering what’s inside: the glassware, the bottles, the small rituals of entertaining,” Corbin See of Sees Design says. “It creates a sense of mystery and restraint that I think interiors benefit from.”