Which one is more enjoyable and easier/better to use for my battle mage, illusion or destruction?

Destruction is offensive, Illusion is defensive

I think in roleplay terms destruction fits a battlemage better than Illusion personally, if you're taking that into consideration.

Illusion imo is the better tree, but destruction is more fun.

Well, your decision ultimately depends on how you want your character to play. In combat, an illusion specialist will have to be pretty skilled, because they can't rely on the magic itself to kill people; that being said, they can use their magic so that their enemies kill themselves..

both are usefull, my opinion ill go with destro

illusion i like best with light/cloth toons sneakl/pure caster types

cheerz

Destruction is kinda of the game's total crap skill for offense. Frankly I would consider alteration for the paraylisis effects and shields instead. Maybe conjuration for the bound weapons and summons over illusion too.

Conjuration is, without a doubt, the most OP magic skill in the game. However, alteration is of limited use to somebody already in heavy armour. The only spells which become useful eventually are dragonskin and the paralysis effect - whereas with illusion you have hands down the best crowd control in the game, and the ability to calm people/animals who attack you - which gives you time to regenerate. Not to mention invisibility and quiet casting.

Illusion is more a stealth skill - you use it so that you can get to places unseen, or eliminate whole armies without ever drawing your sword.

Battlemage uses defensive spells such as restoration and alteration, and heavy armor + weapons. One-handed, heavy armor, restoration, smithing, enchanting, alteration. There's already quite a few skills to focus on.

Illusion is hands down better no contest whatsoever(unless you use some serious exploits for destruction), but it's more geared for stealth based characters.

Except in the games the difference between battlemage and spellsword is arbitrary at best. In Oblivion there were full blown offensive mages in armour calling themselves battlemages, but there was nothing defensive about them.

Pretty much any mage with armour and a weapon is a battlemage.

Destruction, Battle mage uses offensive magic with weapons.

Destruction is the signature skill of a Battlemage. Illusion is better suited to a more fragile mage.

Don't forget the Paralysis spell was moved from Illusion to Alteration in Skyrim. So while Illusion remains great for stealth based characters, it's not as good as it used to be in the previous installments for pure combat.