The Honda Amaze is a compact sedan, the Honda Elevate is an SUV, and the Hyundai Verna is a mid-size sedan. So, they are quite different in terms of body style and their usage. 

The Honda Amaze suits buyers on a tighter budget, and since you’ve shortlisted the Elevate and Verna, we assume your budget is higher and around Rs 20 lakh.

The Hyundai Verna is a well-equipped sedan and works well for city driving. That said, we also suggest you look closely at Elevate. SUVs are generally more comfortable and confidence-inspiring on highways. 

The Honda Elevate 1.5-litre engine paired with the CVT gearbox feels smooth and responsive in everyday city use as well. It also offers a large boot, which is handy for weekend trips and vacation luggage
 

We suggest you wait for the new Skoda Kushaq, which will be launched next month. It has more features and is great on the highway and twisty roads. 
Your budget may limit you to the 1.0 TSI engine, but that’s a really punchy engine mated to a smooth 6-speed automatic box. The Honda Elevate works well as a city car, but it's nowhere near as good as a Kushaq or even a Skoda Slavia on a twisty road. 
 

According to your requirement and among the options you have selected, we would suggest you to go for the Hyundai Creta SX. It scores well above the other options because of the space that it offers. 

Maruti Suzuki Grand Vitara's second row is good for 2, and a squeeze for 3. Honda Elevate's central console protrudes prominently in the second row, compromising rear passenger space.

The Hyundai Creta looks good, is feature-rich, and delivers a comfortable experience for family use, both in city driving and on long journeys. You are familiar with Hyundai’s ecosystem, adding to the ease of ownership.
 

Since you've already owned a Honda car, you might like what the Elevate has to offer. Its ride comfort is its highlight; the high seating will make it easy for your parents to get in and out, and its petrol engine delivers strong performance. 

The Volkswagen Taigun is smaller in size, which makes it a bit easier to park and manoeuvre. However, it doesn't feel as user-friendly as the Honda, since the manual's clutch is a touch heavier, and the automatic isn't as seamless as the Elevate's either. 

Since you're not keen on the Maruti Victoris or Kia Syros, you can also consider the Toyota Urban Cruiser Hyryder.

Both cars you selected have 1.5 naturally aspirated (NA) engines, and the Honda car engine mated to a CVT is clearly the better option for several reasons. 

Firstly, Honda makes the best small-capacity naturally aspirated engines, and for Mumbai traffic, the CVT is a much smoother automatic than the twin-clutch DCA in the Tata. 

Also, the Tata engine, which develops a mere 106hp, is nowhere near as powerful as the Honda engine (121hp). Hence, Honda Elevate is better than the Tata Sierra DCA, which comes with this 1.5 NA engine.