Not sure if I have the class types right but basically both would use destruction, conjuration, heavy armor(maybe light really depends on aeshetics), resto, enchanting and illusion(for destro damage buff). I was just wondering though as I get higher level if casting destruction magic with only one had is even worth the time or if you need to dual cast to really see damage.

Only difference between the two is that the Battlemage used conjuration and not restoration, while Spellswords are the oppostie. In Morrowind Battlemages used heavy armor and Spellswords used Medium Armor (in the case of Skyrim use Light).

The type / weight of an armor makes no difference to a Battlemage / Spellsword. It is just the fact that they wear armor over robes or clothes (like mages usually wear). Normally it would be wise for a Battlemage / Spellsword to wear a lighter armor as their strength (carrying weight) and stamina won't be as strong as a normal warrior. Some may contribute to carrying strength with spells or potions and use heavy armor for it's added defence.
Personally I'd go for light and use alteration on top if needed.