Osaka Unli, Kansai Thru or JR Kansai Pass?

Is it wise to purchase Osaka Amazing pass to visit tourist spots in Osaka? I will be visiting Osaka for a 1 week vacation this November. And below are some places on our list:
1. OSAKA CASTLE
2. Nishinomaru Garden
3. Osaka Bay Area – Tempozan Harbor Village, Osaka Aquarium, temposan Ferris wheel, tempozan marketplace shopping mall)
4. OSAKA MUSEUM
5. SHINSAIBASHI SUJI
6. AMERIKAMURA
7. DOTONBORI
8. MINAMI, NAMBA
9. DEN DEN TOWN
10. UNIVERSAL STUDIOS JAPAN
11. Sumiyoshi Taisha
12. Shinsekai - Kushikatsu
13. Umeda – Osaka Station City, Grand Front Osaka, Umeda Sky Building, Underground shopping mall, shopping arcades,
14. Tennoji - Abeno Harukas - tallest skyscraper in Japan; Shitennoji Temple - inner precinct, Gokuraku-jodo Garden, treasure house
15. Minoo Park - forested valley on the outskirts of Osaka
16. Tenma - Tenjinbashi-suji Shopping Street, Osaka Tenmangu Shrine

We are also planning on touring around Kyoto. Below are the list of places we want to explore.
1. Kyoto Station
2. Kyoto Tower
3. Kyoto Imperial Palace
4. Kyoto Manga Museum
5. Fushimi Inari Shrine /Heian Shrine
6. Arashiyama and Sagano

Day 1,2,3 - Osaka
Day 4 - Universal Studios
Day 5 - Kyoto (day trip only)
Day 6 - side trip to Nara (day trip only)
Day 7 - travel back to Kansai International Airport

We are unsure of which pass is the best for our itinerary.

Thank you in advance!

Regards,
Mariz

You need to read through their site, as Osaka Amazing pass offers 1 day and 2 days, both work differently, and have restriction on transportations, although you can get free entry and discount to places, work out if the prices is fully covered the price of the pass.

You can also consider the Kansai one pass, it's a ICOCA with special discounts and offers free gifts at certain establishments.