What are the practical differences between using bagged vs. loose leaf tea?
Are there differences in quality, caffeine content, etc.? Why?
The differences in quality between teas is usually down to the manufacturer and the product line. As far as I can tell, there is no discernible difference between Twining's English Breakfast tea (for instance) in bags or loose leaf. They are the same leaves, presented differently.
However, and this is the important part, there is a difference in how they infuse. Because of the limitations of the tea bag, and the flow of the water through the leaves, a loose-leaf tea is usually infused more quickly, and possibly better. That is, you get more essence of tea from the leaves into the water. There are different bag designs (pyramid bags for example) which try to bridge some of this gap.
The advantage of the tea bags is that they are easier to work with, as you don't need to strain the leaves out of the water, you can just pick the bag up with your spoon.
There is a lovely essay by George Orwell about making "proper" tea. Some of it is a matter of taste, but his point about the infusion is spot on, in my opinion.
If you look at the higher quality Chinese and Japanese teas you will not (rarely) find them in bags.
For those teas it's important to have nice full leaves that have space to infuse properly, if the leaves are too packed the tasting experience will not be the same.
So yes, higher quality leaves will more probably be sold as loose leaves, but that doesn't mean that all loose leaves are of higher quality.
If you are talking about Lipton, Twinnings and other big brands, well then it's probably the same leaves in a different packaging. If you are talking about for example Longjing then it's loose leaves you want. For Puerh teas you would go for a tea cake
On wikipedia tea page there is a good section about tea bags which I quote:
The use of tea bags is easy and convenient, making tea bags popular for many people today. However, the tea used in tea bags has an industry name—it is called fannings or "dust" and is the waste product produced from the sorting of higher quality loose leaf tea, although this certainly is not true for all brands of tea, especially in the case of many specialty, high quality teas now available in bag form.
Obviously the flavor of loose-leaf tea is usually considered superior, but there are a few other issues to be considered.
(1) As others have noted, most tea bags contain tea that is graded as "fannings" or "dust," which are official terms for smaller bits of tea leaves. (For more information, consult the details on tea grading here.) However, it should also be noted that if you begin with high-quality tea leaves, the fannings and dust will also have better flavor. In many cases, I'd prefer to drink tea made from the fannings of high-quality leaves than tea made with bad-quality whole-leaf tea (grown in a bad location, picked at a bad time, etc.). However, it's rather rare to see fannings of top-quality teas sold with their full identification (estate, flush, grading, etc.) on the retail market, while there are plenty of examples of poor-quality whole-leaf teas on the market.
(2) Because of these smaller pieces, certain elements of the tea will in fact infuse much faster. A number of studies have noted, for example, that tea fannings will release caffeine faster than similar whole-leaf tea. Thus, to answer part of the OP's question which has not yet been addressed, it is possible the tea bags with smaller bits of tea will have a higher caffeine content for the same steep time than whole-leaf tea. Similarly, other chemicals may often be released faster, leading to a different flavor profile. Tea bags may thus require shorter brewing times than loose-leaf to avoid "overbrewed" flavors.
(3) Rare, expensive tea bags sometimes contain whole-leaf or broken grades, rather than fannings or dust. Also, one can buy disposable bags to make your own. In these cases, the tea produced is basically equivalent to brewing tea in an infuser: the tea may infuse differently if it is too crowded or if flow is restricted in and out of the bag/infuser. (However, the vast majority of commercial tea bags do NOT contain whole-leaf tea.)
(4) Relating to the previous point, many commercial producers actually use more broken leaves in their bags than they do in their standard blends. I don't know whether this is because of actual tea graded differently, or if in some cases the producers break the leaves down later in the process before bagging them. Thus, while I agree with another response that a Twinings English Breakfast loose leaf and a Twinings English Breakfast bag will have similar flavors, if you cut open the teabag, you'll often find much smaller bits of tea than you'd find in the can of loose leaf. I assume this is partly to make up for the decreased water circulation in the tea bag: the smaller bits will assure a fuller brewing, even if less water goes through the bag than would circulate around loose tea leaves. Hence, the flavor profile remains similar, even though the tea used looks different.
(5) In addition to the obvious convenience of tea bags (no straining required, portion measured precisely), there may be a couple other advantages. As mentioned above, the smaller pieces of tea in bags may brew more quickly, even if the flavor balance is off. For those people who'd prefer to dunk their tea bag in rapidly for a few seconds before drinking, it's probably more effective than using an infuser of loose leaf. (It's not what I do, but I know many people who do that.) Also, high quality tea bags often are contained in individual sealed packages, which provide a simple way to retain flavorful tea for a long period of time. Loose-leaf teas as well as tea bags will degrade when improperly stored, so a sealed individual packet may also be convenient. (However, on the other hand, whole-leaf tea stored properly tends to remain fresher longer than broken leaves, so expect unsealed tea bags to deteriorate faster.)
With green tea, I find that the green tea in bags tends to develop a very bitter note (which I don't like) much more quickly than loose leaf tea does, and I speculate that this is because the bags contain much smaller pieces of leaf - even down to powder. This leads to a higher surface area to volume ratio, and thus much faster infusing in the bag. Because of this, I find myself unable to infuse bags of green tea properly, and if I really want to enjoy it I should use leaf tea where I can get the flavour without the overwhelming bitterness.
Tea bags are a useful convenience, but if you want really really good tea, use good leaf tea and do it properly.
(Of course some good tea is supposed to be a powder - Japanese matcha springs to mind - but that's not the normal way of things).
When I visited the Boh tea plantations in Malaysia, we were shown the various processes. There, they told us that during separation just before packaging, the full leafs are sorted to be sold as 'loose leaf' tea. Those that get broken during the process get made into so called 'lower' quality tea like bags and powders.
Not sure if it was a marketing ploy or if it's really true, but they claimed that loose leaf was of better quality than bags.
And most really good quality tea you get is loose leaf as well.. So I am inclined to say that..
I drink a lot of coffee and tea, and while I can drink just about any kind of coffee, I can only truly enjoy full-leaf tea. My wife can't tell the difference, so it is possible that I am imagining the better quality of it (or that I have better taste buds!), but just from my experience it is better, hands-down.
However, it is definately better in that the full leaves do not leave as much "residue" in your tea at the bottom of the cup. Crumbled tea leaves can sometimes sometimes leave noticeable specs that settle in the bottom while brewing (especially lower-quality teas). While this does not affect the taste, it is certainly a disadvantage.
I hope this is helpful!
Tea bags are just for convenience. I am an Indian and we normally add tea leaves in boiling water and sugar. My wife relishes green tea and she purchases Twinings and the tea in tea bags is powdered or in fact dust. I would avoid tea bags as much as I can, reason until and unless I brew the tea properly in boiling water I do not find the taste and aroma to the mark.
For low or medium grade tea, do as you like.
For high quality tea, bags are borderline criminal. Since you're paying extra for a fine tea, let the loose leaves diffuse the maximum of their aromatic compounds into the water ! (Thus, tea ball infusers are a shame too.)
But really, try it : brew the same tea in a cellulose bag and at the same time free in a cup, and compare. Since you're making experiments, compare waters (tap, mineral and spring) and temperature. These are the three most important parameters.