The only real difference is Neil Marshall’s Hellboy looks to be a more anarchic R-rated romp, while the del Toro / Perlman variant was more reserved and reverent.
Those movies flourished under the auspices of Ron Perlman as Hellboy and Guillermo del Toro as the director leading the project.
Obviously, the big question here is how Harbour and Marshall’s work holds up to that of the previous Hellboy franchise.