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I think both tools have their own pro and con. Some of the feature, calibre did a better job compare to hercules, and the other way round for some other feature. It's totally up to the user preference.
For sign-off means foundries accept for tape out as foundries will run DRC/LVS for your GDSII as well, so you need to match the tools they use, that's why they release the rule sets for you.
For tools, there are most likely three tools
Calibr@ from me@tor graphics
Dracul@ from Cad@ence
Hercule@ from Syno@psys, which is A@vanti previously
Assura@ is seldom used by ppl as it's not efficient. It's just for running small blocks and small chips as it can integrate normally to Cadence@ layout tool and so you can simultaneously view ur errors online. Others most likely use command mode