The idea of which bowls are "better" is somewhat subjective. But I think they can be divided into four categories:
1. BCS bowls: These games pay the most money, and invite the champions of the major conferences, plus a handful of other highly-rated teams. These bowl games are the Orange, Sugar, Fiesta, Rose, and the new national championship game. They are played on or after January 1.
2. New Year's Day bowls. Playing a bowl game on New Year's Day used to be the gold standard, but since the BCS' reign of terror began, the non-BCS New Year's Day games have fallen off in prestige.
These games invite mostly second- and third-place teams from the Big 12, SEC, and Big Ten conferences; in fact, all eight slots are predetermined based on conference alignment -- there's no way for an outsider to break into one of these games. In my opinion, that makes these games less meaningful. The New Year's Day games are the Cotton, Capital One (formerly Citrus), Outback (formerly Hall of Fame), and Gator bowls.
3. Mid-Tier bowls. I consider a bowl mid-tier if it meets at least one of these requirements: (a) has a long history; (b) is known by a name other than that of a corporation; (c) is in an attractive city for travelers; (d) pays its teams more than the NCAA-mandated minimum; or (e) has tie-ins that will give it Top 25-quality teams most years.
Major-conference teams that appear in these bowls typically finished somewhere between fourth and seventh place in their league. Also, the top teams from "mid-major" conferences have berths into these games.
Bowls in this category include the Las Vegas, Independence, Holiday, Music City, Sun, Liberty, Insight, Hawaii, Emerald, Champs Sports (formerly lots of other corporate names), Alamo, and Chick-Fil-A (formerly Peach) bowls. Bowls with a more tenuous claim to this category are the Motor City, New Orleans, GMAC, and Armed Forces (formerly Fort Worth) bowls.
Please note that this is a broad category, and that some of these mid-tier games are more desirable than others. For example, the Chick-Fil-A and Music City bowls both invite teams from the SEC and ACC, but the Chick-Fil-A Bowl is higher in the pecking order. Thus this game gets stronger teams than the Music City Bowl, and most would consider it the preferable game to be in.
4. Dot-com bowls. In recent years, the number of bowls has increased tremendously. This has created a huge number of new, low-prestige bowl games. Basically, these games don't meet any of the requirements to be a mid-tier bowl, or meet one requirement at best.
These are startup games with no history; they're named solely after corporate sponsors, they're in less desirable travel locations; they pay only the required minimum of $750,000 per team (which means most schools will lose money on the game); and they're so far down in the conference tie-in pecking order that they have little chance of getting a Top 25 caliber team.
Teams in these games are either also-rans from also-ran conferences, or are major-conference teams who barely qualified for a bowl by going 6-6. Even 7-5 major-conference teams can usually make the mid-tier category.
This lowest tier of bowl games consists of the Poinsettia, New Mexico, PapaJohns.com, Texas, Insight, MPC Computers, Meineke Car Care, and International bowls. And as I said earlier, you could also put the Motor City, New Orleans, GMAC, and Armed Forces (formerly Fort Worth) games in this bottom group.
A list of all the bowl games is easy to find on the web. The college football section of any major sports news website would have it.