A lot has changed between Morrowind and Oblivion when it comes to the Battlemage and the Spellsword classes.
The Morrowind Battlemage:
Battlemages are wizard-warriors, trained in both lethal spellcasting and heavily armored combat. They sacrifice mobility and versatility for the ability to supplement melee and ranged attacks with elemental damage and summoned creatures.
- Specialization: Magic
- Attributes: http://elderscrolls.wikia.com/wiki/Intelligence_(Morrowind), http://elderscrolls.wikia.com/wiki/Strength_(Morrowind)
Major Skills:
- http://elderscrolls.wikia.com/wiki/Alteration_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Destruction_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Conjuration_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Axe_(Skill)
- http://elderscrolls.wikia.com/wiki/Heavy_Armor_(Morrowind)
Minor Skills:
- http://elderscrolls.wikia.com/wiki/Mysticism_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Long_Blade_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Marksman_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Enchant
- http://elderscrolls.wikia.com/wiki/Alchemy_(Morrowind)
The Morrowind Spellsword:
Spellswords are spellcasting specialists trained to support Imperial troops in skirmish and in battle. Veteran spellswords are prized as mercenaries, and well-suited for careers as adventurers and soldiers-of-fortune.
- Specialization: Magic
- Attributes: http://elderscrolls.wikia.com/wiki/Willpower_(Morrowind), http://elderscrolls.wikia.com/wiki/Endurance_(Morrowind)
Major Skills:
- http://elderscrolls.wikia.com/wiki/Block_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Restoration_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Long_Blade_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Destruction_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Alteration_(Morrowind)
Minor Skills:
- http://elderscrolls.wikia.com/wiki/Blunt_Weapon
- http://elderscrolls.wikia.com/wiki/Enchant
- http://elderscrolls.wikia.com/wiki/Alchemy_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Medium_Armor_(Morrowind)
- http://elderscrolls.wikia.com/wiki/Axe_(Skill)
The Oblivion Battlemage:
"Able to resolve most conflicts with either spell or sword. They are a deadly mix of scholar and soldier."
Specializationhttp://elderscrolls.wikia.com/wiki/Battlemage?action=edit§ion=2
- http://elderscrolls.wikia.com/wiki/Magic
Favored http://elderscrolls.wikia.com/wiki/Attributehttp://elderscrolls.wikia.com/wiki/Battlemage?action=edit§ion=3
- http://elderscrolls.wikia.com/wiki/Intelligence
- http://elderscrolls.wikia.com/wiki/Strength
http://elderscrolls.wikia.com/wiki/Skillhttp://elderscrolls.wikia.com/wiki/Battlemage?action=edit§ion=4
- http://elderscrolls.wikia.com/wiki/Alchemy
- http://elderscrolls.wikia.com/wiki/Alteration
- http://elderscrolls.wikia.com/wiki/Blade
- http://elderscrolls.wikia.com/wiki/Blunt
- http://elderscrolls.wikia.com/wiki/Conjuration
- http://elderscrolls.wikia.com/wiki/Destruction
- http://elderscrolls.wikia.com/wiki/Mysticism
The Oblivion Spellsword:
Specializationhttp://elderscrolls.wikia.com/wiki/Spellsword?action=edit§ion=7
- http://elderscrolls.wikia.com/wiki/Magic
Favored attributeshttp://elderscrolls.wikia.com/wiki/Spellsword?action=edit§ion=8
- http://elderscrolls.wikia.com/wiki/Endurance_(Oblivion)
- http://elderscrolls.wikia.com/wiki/Willpower_(Oblivion)
Major skillshttp://elderscrolls.wikia.com/wiki/Spellsword?action=edit§ion=9
- http://elderscrolls.wikia.com/wiki/Alteration_(Oblivion)
- http://elderscrolls.wikia.com/wiki/Illusion_(Oblivion)
- http://elderscrolls.wikia.com/wiki/Blade
- http://elderscrolls.wikia.com/wiki/Destruction_(Oblivion)
- http://elderscrolls.wikia.com/wiki/Heavy_Armor_(Oblivion)
- http://elderscrolls.wikia.com/wiki/Restoration_(Oblivion)
- http://elderscrolls.wikia.com/wiki/Block_(Oblivion)
If you're confused, maybe it's worth debating on what fits a proper battlemage more and what fits a proper spellsword more.