The Talenta Sharrash has errata that changed it to 19-20/x2.
+19 or so is the turning point. If the character has less bonus damage than that, the great scimitar is a bit better for damage. If the character has more, then the 19-20/x3 katana is better. Keep in mind that the katana keeps getting better as you add more bonus damage. At +40 damage the 19-20/x3 katana would do 49.48125 versus the great scimitar's 48.39375, for a difference of 1.0875. It's not much, and most people wouldn't even notice the overall difference between the weapons, but that's what it is and that's exactly how most other weapons work. Heck, the difference between a scimitar and a longsword at +40 damage is only 0.915, assuming base crit.
The calculations are for the long haul by the way. A 20th level strength-based melee character had better have more than 24 strength and will definitely have more than +20 damage on his weapon. If you're going to talk about things at different levels, specify what those circumstances are and I'd be happy to post the numbers.
Comparing an 18-20/x3 katana against the great scimitar at +30 damage shows a difference of 3.68625. Add Keen to both and the difference is 8.325 at +30 damage. In other words, (and what I should have said from the start) making the katana 18-20/x3 entirely nullifies the great scimitar. It'll have the same crit range and it does more crit damage. The tradeoff is a barely noticeable 1 lower average damage against stuff that can't be crit.
Let's go with the scimitar getting 2d6 compared to your katana's 1d8, just to see how things change. Starting off at +0 damage, the scimitar does 7.6125 and the katana does 5.535 for a difference of 2.0775 in favor of the scimitar. Going up to +20 damage, the scimitar is at 29.3625. Your katana is at 30.135, which means the difference is .7725 in favor of your katana. The size difference doesn't really change the fact that your katana simply scales better than the scimitar does.
Adding keen only makes the scaling even better for the katana. A keen 2d6 scimitar starts at 8.5575. Your katana starts at 6.78375, for a difference of 1.77375. Go up to +20 damage on both though, and the scimitar is at 33.0075 while the katana is at 36.99375, a difference of 3.92625 in favor of your katana. Once again, your katana simply outdoes the great scimitar.
Since you mentioned the sharrash though, let's look at how it does:
At 1d10 it has a base average damage of 5.5. Assuming it is 19-20/x4 crit, factoring in crits and the automatic fails on a 1 shows it does an average damage of 6.77875 right from the start. Your katana is doing 4.305, for a difference of 2.47375. Adding +20 damage, we see that the sharrash is at 31.42875 and your katana's at 28.905, for a difference of 2.52375. That's greater than the previous difference, which shows that the sharrash with base crit will always do better than your katana. Add keen to both and they start off at 8.31875 and 5.27625 respectively, for a difference of 3.0425. Going up to +20 damage, the difference becomes 3.1425, so once again we see the sharrash without errata always does better than your katana.
What's my point with all this? Think carefully about what crit numbers you give your weapons. It's quite possible the designers realized the sharrash scaled exceptionally well and decided that the scaling and reach and ability to make trip attacks made for a more powerful weapon than they actually wanted to produce.