First off, both the scooters you are looking at are proven products from reputed Japanese makes, so in the end, whichever one you decide to go with, you should, by and large, have a good experience.
The Suzuki Access is a stellar family scooter option because it has traditional strengths like comfort, practicality, fuel efficiency and a reputation for reliability. Also, it is rather fun to ride with its peppy engine and balanced handling. It also has a bigger underseat storage area, which is a USP in comparison to the Yamaha Fascino 125.
The Fascino’s strong points are that it is exceptionally fuel efficient and it is one of the lightest two-wheelers on sale in the country today. If those are important to you and your wife, then the Yamaha would make for a sensible purchase.
A test ride of both will help you decide which is the better fit for you.