I'd endorse the low-carb diet option. Worked for me.
Low GI appears to have no useful effect for me - some things that should be slow are fast and vice versa, and things that should be the same work at different rates. I gave up on it years ago. Your experience could be different.
If you're thinking about how low your low-carb should be, there's a few things to think about.
Firstly - what are you trying to achieve? Is it BG control/reduction, or that and weight loss? How quickly do you want to achieve it? What can you really cope with? No point starting out with a target that you simply can't reach.
Secondly - it's carbs, not just sugar. So potatoes and most root veg, bread, pasta, rice, most fruit, pastry etc - all are heavy carb items - bread and potatoes are generally around 60% carb. But you need to consider not just how many carbs are in a particular food, but how much of it you're likely to eat. So (for example) 10g of a 25% carb item has fewer carbs (2.5g) than 100g of a 8% item (8g). Obviously if you go down this route I would prioritise removing high carb, high intake items first.
I normally aim for around 20g carb/day, which means carb-heavy foods are not an option. My carb intake is almost all from green veg.
And if you do cut out a lot of carbs you will probably have to up your protein and fat intake to compensate. You might also need to take extra salt - again caused by reducing carbs, which tend to come bundled with salt.
Best of luck.