Again, you lot are acting like the SI is nothing without her ghosts, this couldn't be further from the truth.
The Sith Inquisitor is considered to be the weakest members of the Dark Council without her force ghost buddies/artifacts. Which need time to recharge and be reined back in.
With them she 's one of the most powerful sith in the world sans Emperor, without them she's one of the top 10 probably.
The Jedi Consular is The Strongest member of the Jedi Council. Bar none. You are a strange anomaly that can tap into the force in a way that shouldn't be possible, calling more power to you than any Jedi of your training should be able to. You are the anti-Emperor. You're the Exile Part 2. The Force flows through you naturally and when you eventually die, you'll leave a force ghost without having to try.
Given thousands of years the Jedi Consular could, without any outside influence, just self training, meditation, etc likely match the Emperor at his peak. They're that gifted.
The issue is that you don't have thousands of years between when the Inquisitor and Consular fight. So it comes down to Sith Artifacts and Ghosts vs. Raw Talent. I think a 'proper' Consular would likely lose the conflict - a proper Consular would not take the final blow even if they could, they would offer redemption, they would try to show the Inquisitor the light, and to take them to the Order.
The Inquisitor, even lightsided, would be less inclined to show mercy in a way that leaves them open to reprisal (and the Consular less likely to try and attack with their back turned). A light sided Inquisitor might claim the consular was 'worthy' but should train more, and that they await their next fight, and then leave. A proper lightsided Consular wouldn't strike the enemy with their back turned.
Of course, two darkside characters would come down to probably them both killing each other. Or the proper end, the Consular dies, but the inquisitor is left broken and exhausted, and her force ghosts rebel again, tearing her body and mind apart as she lay next to the dead Jedi.