Generally speaking, that depends on a number of factors, the quality of the tea in the bags, what type of tea, how long you brew it, and what temperature you brew it.
Loose tea is the whole or mostly whole leaves of the Camellia sinensis, dried, rolled, and processed in various ways. It makes a better tasting tea for several reasons. Whole leaves have more flavor because they have less surface area exposed to the air. Air makes tea go stale and lose flavor. Their size also causes them to brew more slowly, thus releasing fewer tannins. Tannins are what makes tea bitter when you drink it. Loose tea also allows the water to circulate through to tea. If you use a class teapot, you can actually see the tea leaves unfurl in what’s known as “the agony of the leaves.” This unfurling releases more flavor in the process.
However, it’s possible to get a bad loose leaf tea in some stores, especially the types of stores that sell “closeout” products. Sometimes the tea is very old or has been improperly stored. It could have just been inferior tea to start with.
All that aside, there is nothing wrong with brewing tea with teabags. It may not be the “perfect” tea experience, but you can get good tea from teabags if you brew it right. In the past, the tea in teabags was dust or fannings, tiny bits of tea that instantly released tannin as soon as it was hit by boiling water. These days tea companies are putting a better quality of tea into their teabags. If you tear one open, you will see that the are larger pieces of tea leaf inside than there used to be. However, they are still smaller than loose tea. This means you have to modify how you brew the tea if you don’t want it to turn out bitter.
First, unless you use 50 or so teabags a week, avoid the large boxes of teabags. They tend to go stale if not used up quickly. Buy the teabags in boxes of no more than 20. Take them out of the box and store them in a tin with a tight lid. Shorten your brewing time. Unless the leaves in your teabag are whole or almost whole, they will brew much more quickly than loose tea. If you would brew it for 5 minutes as loose tea, brew it only 2 or 3 minutes in teabags. Make sure you are using the right water temperature for your tea. Black, green, oolong, and white teas all brew at different temperatures.
If you are unsure of the temperature of the water you should use or how long to brew the tea, check the label on the tea package. Chances are that the tea company that made packaged it tested it out beforehand and know what time and temperature is needed.
Therefore, if you don’t have access to loose tea leaves, or you think they’re too costly, or you just don’t want to go to the trouble, there’s nothing wrong with drinking tea made from teabags as long as you brew it right and you enjoy it.