First off, if you like it, by all means drink it.
There’s not a massive difference in taste between different types of green tea, but it’s one that most people could probably distinguish. The main factors that affect the flavor of the leaves themselves are where it’s grown, how it’s grown, and when it’s harvested. (Further processing has an effect, but I’m sticking to green tea only, which has minimal processing).
The factors after that are the ones you’re more likely to be dealing with here. The age of the tea is probably the biggest, since you want green tea to taste and be fresh. How it’s packaged and whether it’s mixed with other tea will also make a difference.
Think of it about the way you would freshly-milled vs. already-ground spices: They’re both the same thing, but one is going to be missing some of what the other has. Tea doesn’t necessarily age as poorly as some spices do, to be fair. With few exceptions, bagged tea is made from broken leaves, so as a rule it will undergo more exposure to air and thereby be less fresh than whole leaf.
Personally, I’d rank them something like this:
Mass-produced pre-made tea (e.g. Snapple). Most likely sweetened and mixed with other flavorings to produce a consistent product that is almost, but not entirely unlike tea.
Bagged broken-leaf tea, ranked roughly by price. I don’t know how expensive Luzianne is, but I’m guessing it’s somewhere in this group.
Loose/whole leaf tea. This covers a wide range, and some preparations get rather fancy. Bad loose tea can easily be worse than good quality bagged tea, but even then the whole leaf is going to last longer.
As an aside - matcha is a Japanese powdered tea that’s more of a specialized product. Just because it’s powdered doesn’t make it bad; what I’m comparing is mainly if you took the same tea leaves and delivered them in these different ways.