I think each set of towers should have different attributes to make them more meaningful

Let's face it, right now towers are boring pits of gold that you need to defend/destroy.

Tier One towers: I like the way they function right now. Basically a buffer to let you farm up to your first item safely. Strategically you know you are probably losing all of these, it's just a matter of when you want the enemy team to get the gold/they manage to pry it from you. Consider a holding/retreating action before getting to the castle moat. One change: When an enemy champion receives aggro and there are more than two enemy champions in range that are potentially aggroable the tower now deals AoE damage. Why? 2v2 outplays and towerdives cans till be a thing, a little help for the 3v2 and 4v2 shenanigans.

Tier Two towers: First 'serious' line of defense to the base. Each tower can contain a charge that is activated by 2 players on your team selecting the charge. This charge fires a long range attack against enemy champions and affects a true damage AoE. range/dmg of Jayce Q. Charges moderately slow to stack, roughly the time between siege minion spawns.

Tier Three Towers: These should be a bigger problem to get through. No one would build weak ramparts to their castle! These towers should have about twice the HP of Tier 1 turrets, if not more. Having champions under this tower should be a meaningful preventative. Champions under these towers receive health and mana regen buff of 100x% Having 3 or more champions at these towers spawns defenders a la zzrot portal.

Nexus Towers: Lazers Lazers and more lazers. Every time a nexus tower kills or gets an assist off of killin an enemy (minion, pet, champion) it's beam splits and it gains another beam. When it kills an or assists enemy champion it also regains 5% hp. Edit- Context- You should have to build up a huge minion wave or have champions present to take these towers. It's your friggin NEXUS bro, get some defense on it.

Other tower based ideas: Teams can collect rubble from their destroyed towers to rebuild one of them. 3 destroyed towers= 1 rebuilt could be a good ratio. Towers drop health/buff packs upon destruction that can be picked up by either team. Towers are worth more gold based on the number of minions/champions it's killed.

Edit for more ideas- Teamwide buffs as tower tiers fall.