I am confused between the Kia Clavis HTX+ and the Toyota Innova HyCross base model, as both are similarly priced. This will be a chauffeur-driven car. Which one should I choose?

Go for the Kia Carens Clavis HTX+. For the price, it's a far better value for money, and remains an excellent chauffeur-driven car. 

You get a wider choice of engines and gearboxes, where the base Innova is only available in Petrol CVT guise. Also, you will get far more features in the fully loaded Kia car than in the base model Toyota Innova HyCross, which is geared more to fleet operators. 

And finally, the fuel economy on the Innova petrol is notoriously low, given it is a large vehicle with a large petrol engine. Moreover, any of Kia's powertrains would offer higher mileage.