Currently PoW selects a dictator that unilaterally decides what is or is not included within a block. Block winners can include blatant double spends or withhold transactions should they choose.
Avalanche would instead leverage PoW, not to choose a dictator, but to choose the participants within an assembly that decide amongst themselves what transactions will be included within a block. Double spends are impossible for those transactions that have gone through the Avalanche process. Should a miner include a double spend, the other miners orphan the block by refusing to build on top of it.
Avalanche still leverages majority hashpower that operates within the particular set of consensus rules (Avalanche would be an additional portion of that rule set). For those critics that say Avalanche betrays PoW, PoW is still valid within the given ruleset; however, PoW means nothing when operating outside of it (Like RBF transactions not being valid within BCH even though BTC has by far more PoW).
There is nothing 'centralizing' about Avalanche, in fact, it is even more decentralized. Instead of having one unilateral entity deciding what is included within blocks, you have a group of miners deciding what will be added to the blockchain.