The list of 20 items they could choose 10 from is (number on the right is how many times it was claimed by Alone folks):

Code:
1. Ferro Rod (10)
2. Regular Knife (9)
3. Large Knife (Khukuri)
4. Axe (10)
5. Saw (6)
6. Leathermen Multi-Tool (1)
7. Sharpening Stone (2)
8. Sling Shot (2)
9. 300 yards single filament line with 25 assorted hooks (10)
10. 550 paracord – 20m (5)
11. 3.5lb wire (1)
12. 2 Qt Pot (10)
13. Canteen/Waterbottle (3)
14. Gill Net (4)
15. Bow & 6 Arrows (4)
16. 12×12 ground Tarp (6)
17. Extra Tarp (1)
18. Sleeping Bag (10)
19. Bivy Bag (2)
20. Emergency Rations (3)

My 10 items would be:
1. Ferro Rod (10)
2. Large Knife (khukuri) (1)
3. Axe (10)
4. Leatherman Multi-Tool (1)
5. 300 yards single filament line with 25 assorted hooks (10)
6. 3.5lb wire (1)
7. 2 Qt Pot (10)
8. 12×12 ground Tarp (6)
9. Extra Tarp (1)
10. Sleeping Bag (10)

Not taking and why:

2. Regular Knife (9)
- Large figured blade of khukuri is very versatile + 2-3 LM knifes - should be more than enough.

5. Saw (6)
- The axe provided is good. I'm good with axe even with 1' wide logs.

7. Sharpening Stone (2)
- LM has good files.

8. Sling Shot (2)
- Hunting is time consuming, will relay on snares, or make a bow or a sling for small game.

10. 550 paracord – 20m (5)
- fishing line gives more than twice as much cordage: 300m>160m (20m*(7 strands+1 shell))
- plus hooks for fishing, bird traps, fishing spear tip (get 3, anneal, straighten with LM, quench).
- The fishing line has a large plastic spool as a bonus.
- Tarps could be the source of thick cordage as well if needed.

13. Canteen/Water bottle (3)
- the pot provided is good, has larger volume, and pan lid;
- can make a bark/log canteen using LM, or rig the water transporting/storing pouch/pool from the second tarp.

14. Gill Net (4)
- too small, tide traps are way better. Can be made from the fishing line if absolutely necessary.

15. Bow & 6 Arrows (4)
- Can be made with wood and fishing line. But hunting is still seems ineffective there.

19. Bivy Bag (2)
- Good while you're in the process of making the stationary shelter, but a cocoon with similar or better properties can be rigged from the second tarp, which is more versatile as well.

20. Emergency Rations (3)
- Just eat plenty before you go (cheating? 10 items limit out of 20 fixed list is cheating too)... smile