Bitcoin’s proof-of-work (PoW) vs Ethereum’s proof-of-stake (PoS).

1.  Definitions used in the literature 

- Finality 
  - PoW: probabilistic. The chance of a reorganisation decays exponentially with each added block. 
  - PoS (Gasper in Ethereum): deterministic or “economic” once two consecutive epoch checkpoints are justified; reversions would slash at least one-third of all staked ETH.

- Security properties 
  - Safety / common-prefix: honest nodes agree on a single history. 
  - Liveness / chain-growth: honest transactions eventually appear on-chain. 
  - Threat model: an adversary controls a fraction of hash rate (PoW) or stake (PoS) and may delay messages within network bounds.

2.  Bitcoin PoW according to scientific papers 

- Safety and liveness proofs exist in the “Bitcoin backbone” model; they hold provided the adversary controls less than half the global hash power and network delays are moderate. 
- Finality in practice: six confirmations (≈ one hour) produce a re-org probability below 10⁻⁵, but economic analyses show that if block rewards and fees fall, achieving the same assurance could take days or even months because the cost to attack decreases while honest miners’ incentives shrink[^1][^2]. 
- Accountability: none. Attackers who succeed keep their mining rewards; there is no on-chain slashing. 
- Long-range or equivocation attacks are inherently impossible because rewriting history requires re-doing PoW from genesis.


3.  Ethereum PoS after the Merge 

- Casper FFG + LMD-GHOST (collectively “Gasper”) guarantees safety if less than one-third of stake violates the rules; conflicting finalised checkpoints cannot both exist unless violators are slashed[^3][^4]. 
- Deterministic finality: two epochs (2 × 32 slots) ≈ 12–15 minutes in a synchronous network[^4]. 
- Liveness: needs at least two-thirds honest stake. Several works describe attacks that can delay but not violate finality, e.g. balancing or staircase attacks[^5], and routing-level partition attacks that drop attestations[^6]. 
- Additional considerations 
  - Weak subjectivity: a node joining for the first time must obtain a recent checkpoint to avoid long-range forks[^7]. 
  - Ongoing hardening: proposals for re-org-resilient modifications show safety under synchrony even when attackers equivocate[^8].


4.  Direct comparison drawn from the literature 

- Speed of finality 
  - Bitcoin: probabilistic, tens of minutes to hours; grows longer if miner incentives weaken. 
  - Ethereum: deterministic after ≈ 13 minutes. 

- Objectivity vs subjectivity 
  - Bitcoin: anyone can verify the heaviest valid chain without external help. 
  - Ethereum: requires a trusted recent checkpoint to rule out long-range attacks. 

- Adversary threshold for safety 
  - Bitcoin: honest hash power must exceed 50 %. 
  - Ethereum: honest stake must exceed 66 % (safety holds up to 33 % faulty stake). 

- Accountability 
  - PoW: none. 
  - PoS: slashing burns misbehaving validators’ stake. 

- Extra attack surface 
  - PoS introduces long-range, equivocation and routing attacks not present in PoW; scientific countermeasures exist but add protocol complexity[^6][^8]. 

A recent survey that collates many of these results concludes that PoS “matches PoW security only after additional layers of complexity and social coordination, while gaining significantly faster finality”[^7].


5.  Answer to the original question 

Better finality:

Yes, Ethereum’s proof-of-stake reaches deterministic finality in about 13 minutes, whereas Bitcoin’s proof-of-work offers only probabilistic finality that can require an hour or more and may lengthen if mining incentives deteriorate[^4][^1]. 

Better security:

neither system dominates on all fronts. 
  - PoW provides objective security and is immune to long-range or equivocation attacks as long as honest hash power exceeds 50 %. 
  - PoS achieves similar safety with only two-thirds honest stake and adds slashing-based deterrence, but it is weakly subjective and opens additional attack vectors that must be mitigated[^5][^6]. 

In short, choose PoW if you value simplicity and trust-minimised bootstrapping; choose PoS if you prioritise quick, economically guaranteed finality with on-chain accountability.

[^1]: [Beyond the doomsday economics of "proof-of-work" in ...](https://www.bis.org/publ/work765.htm)
[^2]: [Beyond the doomsday economics of “Proof-of-work” in cryptocurrencies](https://www.bis.org/events/confresearchnetwork1909/auer_pres.pdf
[^3]: [1710.09437] Casper the Friendly Finality Gadget - arXiv.org](https://arxiv.org/abs/1710.09437)
[^4]: [PDF] arXiv:2210.16070v2 [cs.CR] 14 Sep 2023](https://arxiv.org/pdf/2210.16070)
[^5]: [2110.10086] Three Attacks on Proof-of-Stake Ethereum](https://arxiv.org/abs/2110.10086)
[^6]: [Routing Attacks in Ethereum PoS: A Systematic Exploration - arXiv](https://arxiv.org/abs/2505.07713)
[^7]: [Unsealing the secrets of blockchain consensus: A systematic comparison ...](https://arxiv.org/html/2401.14527v1)
[^8]: [[PDF] Towards a Reorg-Resilient Solution for Ethereum Proof-of-Stake](https://eprint.iacr.org/2025/097.pdf)