Hi HollyKnight:
Here's a top level bulleted list of differences:
1. Characters
TOS - Adama, Apollo, Starbuck (male), Tigh, Athena, Boomer (male), Jolly, Greenbean, Serina, Boxey, Baltar, Cassiopeia, Zac, Centurions, Imperious Leader, Lucifer
Mini - Adama, Apollo, Starbuck (female), Tigh, Boomer (female), a mention of Jolly, Boxey, Baltar, mention of Zac, Tyrol, Lt. Helo, President Roslin, Six and the other humanoid Cylons.
2. TOS - Colonies are already at war. Colonial fleet destroyed in an ambush, the colonies by sneak attack under pretense of a peace armistice arranged by Baltar. Mini - Colonial fleet and colonies destroyed by sneak attack, with Baltar an unwitting accomplice.
3. TOS - Galactica a fully operational battlestar with full complement of Vipers. Mini - Galactica is an old battlestar on verge of de-commisioning.
4. TOS - Battlestars, Vipers, Basestars, Cylon fighters all have laser cannons. Mini - bullets / missiles.
5. TOS - no Ragnor space station. Mini - Ragnor.
6. TOS - civilian government IMHO is "stupid." Mini - President Roslin is a level-headed politician.
There are of course a ton of other differences, but I think these are the main ones. Anyone else want to chime in here?