First of all, I'm not a BSV promoter, I'm just interested in BSV's claim as the real bitcoin, from a noob bitcoin enthusiast (i.e., my) perspective.
For you who did not know, BSV is an abbreviation for Bitcoin Satoshi Vision. It was a fork of Bitcoin Cash network on November 15, 2018. Both sides claimed to be the real bitcoin, but it should be only one that is real, or is it?
Source: bitcoinsv.io
BTC - BCH Fork
It was all started with SegWit and block-size debates. BCH side argued that the removal of signatures means alteration of the original Bitcoin protocol. Meanwhile, the BTC side wanted to enable the side-chain (i.e., lightning network) instead of scaling on-chain. If you read Satoshi's whitepaper carefully, BTC side was indeed changed the Bitcoin protocol from its original design. Bitcoin was meant to be scaling on-chain, at least from 2008 Satoshi's vision/opinion. Since Satoshi is no longer here, we don't know if his vision remains the same, or maybe he would approve SegWit?
BCHABC (BCH) - BCHSV (BSV) Fork
The drama continues. This split was mainly caused by (1) OP_CHECKDATASIG and (2) Canonical transaction ordering (CTOR) that was proposed by ABC side. SV side argued that OP_CHECKDATASIG was actually "OP_BUCKETSHOP" and claimed CTOR showed lacks of demonstrated benefit (and risky). SV side wants to lock the protocol so that business/developers could freely use the BSV network as their base layer*, unlike the ABC side who planned to tweak the protocol.
*This is because they already planned many on-chain developments to improve the usability of BSV.
Noobs Verdict
If you only count Satoshi version 2008-2010, then Bitcoin SV is clearly the closest implementation of Satoshi's Whitepaper. However, Satoshi is a human, and perhaps he will learn more new things to modify his whitepaper. We should realize that 2017 is different from 2008 when he wrote the whitepaper.
Maybe instead of guessing, why don't we ask Craig? What if Craig S. Wright really was Satoshi Nakamoto?