Are colonies who negotiated with their former colonial power for independence better off than those Colonies who won independence through a liberation war?

The only way to answer a question like this usefully is to constrain it to a fairly specific historical moment. I don't think you can derive a generalized theory of "how best to get your colonizer to grant you independence" by mixing in the United States, Haiti, Algeria, Kenya and Malaysia, for example.

So just focusing on modern European imperialism in Africa, the Middle East, South Asia and Oceania? I'm not sure it's easy to come to any straightforward conclusions.

Much depends on what you mean by "better off", for one. There was a liberation war in Kenya, and the people who fought in that war (the Mau Mau Rebellion) were very harshly treated by the British, whereas to a relative degree, people pressing for independence in Tanzania, Zambia and Ghana were not treated so badly. Badly here means "hanged and tortured", as per David Anderson's Histories of the Hanged and Caroline Elkins' Imperial Reckoning. This seems like a bad outcome for the people involved. But if you mean were the economic and political outcomes X decades after decolonization better for the two countries which had a more or less negotiated hand-over of power vs. the country that had a violently suppressed liberation war and then a negotiated hand-over of power, not really? Ghana's outcomes look somewhat more favorable at the moment but I don't think that has to do with the decolonization process--it's a more recent divergence between these three countries.

Throw Zimbabwe into the mix, where a liberation war was in some sense victorious, and the case for liberation war seems to take a pretty hard blow. But throw in Mozambique, also decolonized through a liberation war, and the outcomes seem better today, though they didn't seem that way 20 years ago.

The problem is that what colonizers do to various former colonies during decolonization is part of the picture. Famously for example, France offered a peaceful mode of decolonization in West Africa via a vote that offered continued association with France and tied the currency of the new states to the French franc. Guinea under Sekou Toure voted "no" and was harshly punished for it--the French sabotaged infrastructure in a rapid withdrawal. Congo was technically a "peaceful" negotiation but the Belgians (and then the US and other Cold War powers) meddled extensively in the transition, arguably sabotaging any hope of the new independent regime succeeding.

I think you have to stop thinking that there's a simple binary here of negotiation v. armed struggle that yields to predictable general models of eventual outcomes. How a colonizer withdrew its authority is significantly variable within various 'negotiated' transitions in Africa, Asia and the Middle East, as well as in the conclusion of armed struggles.