Caveats: In my humble opinion, "Old School" gaming was neither better, nor worse than today's games. It was different though.
When I think of "Old School Gaming," several things come to mind:
* Rules were more suggestions than absolutes: the first gaming systems did not have the tightly written rules that are as focused as the fifth and sixth generation games tend to be. By necessity, the GM/DM/Ref had to do some interpretation. That was the norm. Things were looser in some ways and more physics based. While there was not a chair listed in the weapons table, every 1st Ed. (AD&D) DM knew what damage dice he or she was going to use if the PC picked up one and used it in a bar fight. This also motivated some of the "serious" GM/DM/Ref's to learn about things like plate techtonics and astro-physics. You would have been unlikely to see characters that can move at a much higher rate of speed skipping across diagonals than in ranks and columns. (In some of the newer, tile-based FRPGs you can move a certain number of tiles in any direction that means that you are moving at 1.4 times your regular rank and file speed when moving on diagonals.)
* The base rules tended to try and cover more ground and situations: take a look at a 1st Ed. (AD&D) Dungeon Master's Guide. It is an amazing collection of facts, information, and suggestions across an encyclopedia of topics, because the DM was expected to be able to ad lib in a role-playing setting across the entire universe of situations that the PCs might push the session into. Also, look at the spell lists that came out with the first and second generation of fantasy RPGs. The non-combat spells tended to have longer durations and apply to more non-combat situations than some of the fifth and sixth generation games (at least in the core rules).
* The production quality of commercial gaming materials was substantially less than today: you used to be able to buy a whole campaign setting from Bob B. and gang at the Judges Guild for ten dollars! Really! The City State of the Invincible Overlord was just an amazingly fun setting, and you could buy it and the sewers underneath for less than $25 all together. By the by, you could play in that setting for years of real and campaign time. It was easier on the pocketbook to break into DM/GM/Ref'ing back then because of the lesser cost of gaming products. That also meant that DM/GM/Ref's would often take up calligraphy and cartography to make cool props and nice maps for their players.
* The games tended to worry less about internal logic and sweeping stories: it was the norm to find dungeons populated with an improbable mish-mash of critters in an impossible eco-system. The average session tended to be "kill things and take their stuff." The local city's structure was based on the whim and inclination of the DM/GM/Ref.
* Player Characters were special and differentiated: PC classes and races were not all identical templates with different plug-ins of the same basic power level. Look at 4th Ed. D&D. The basic template for the characters are all the same; you plug and play with different skill trees and encounter and daily based powers, but at their core every class is consistently the same. In AD&D, the mage took longer to level, but that same mage was vastly more powerful at higher levels. In Traveller, a psionic character was rarer and had to be more cautious, but could do things that other characters could only dream of doing. If you were drained to zero level in the original AD&D, you became an average person, incapable of progressing as a player character.
* The link to "classic" literature was more direct: the Lord of the Rings, the adventures of Conan, etc. were evident in the early FRPGs. The influence of MMORPGs and Anime have made the connection less direct. There are more direct game tie-ins to current literature now, e.g., Firefly RPG, Fire & Ice RPG, etc. Additions to games like re-charging powers (e.g., Warhammer FRPG 3rd Ed.) or encounter powers (e.g., 4th Ed. D&D) fit better with a generation that has grown up playing Everquest and WoW, but they fit less well with some of the fantasy and science fiction classics that some of the older gamers grew up with.