What do you mean by 'more effective'?
I see that there are other answers (and some of them are excellent from a point of view of Societal commentary.)
However - I want to do a semi-Frame Challenge as to what you mean by the most Effective?
In Tank enthusiast circles - when inevitably the discussion on 'Which Tank is the best tank' comes up - there will be the obvious fanboys and fangirls - but then there is always one Sage old-guy who points out that the best tank is the one the suits the needs of the Terrain it was designed to fight on, the Mission that it was designed to support and the Doctrinal requirements of the Army that fields it (and usually that guy is named 'The Cheiftain').
In the same way with Small Arms - we often hear that the AR-15 is the deadliest rifle ever - when the reality is that it is a balance of compromises that gives the most amount of bang within a 0-400m distance that it was designed to operate in.
Is an AR15 more effective than an ICBM equipped with Thermonuclear warheads? - depending on your criteria for effectiveness it could be Yes, it could be No.
When we judge effectiveness there are the obvious criteria:
- Effect down range
- accuracy
- cost
etc.
But then there are also the less-obvious criteria.
- Social acceptability
- risk of escalation
- risk of tech being captured
- risk of friendly fire/collateral damage
etc.
If we look at say a certain conflict ongoing in a certain region between a certain Nation in response to a certain terrorist attack:
Carpet bombing an area and reducing it to rubble is the most effective means in one sense because it means you are not putting boots on the ground and risking the lives of your service men and women.
However - doing so has lots of collateral damage, galvanizes the population against them, increases support for said terrorist faction and creates lots of disturbing images that can be used to create international pressure. In that sense, it is the least effective method.
What I hope to have demonstrated is that when you are choosing a weapon to deploy - there are a number of questions you want to ask and that determines what is the most effective. Working backwards from what the Kaiju can do but other weapon systems can't do (and vice versa) gives you a series of points to work out what the Aliens criteria for effectiveness is and why they choose the Kaiju.