How does the capacity (kVA) of a UPS affect my power consumption?

In your case, there are two important parameters for a UPS.

Power (kVA) and Energy (VAh).

Power is a measure of how much instantaneous power the UPS can source. This is important based on how much power the attached devices need to draw.

Energy is important because it dictates how long the UPS can continue to run. This is largely dictated by the amount of the energy storage (batteries) in the device.

So, if the Battery Bank (energy capacity) is the same size, but the available power is higher than the devices you need to connect, then this device is equivalent for your needs.

There is a chance that the electronics that allow it to deliver more power, may make it less efficient in your use case, it is unlikely to be significant.

You probably got a good deal. It is possible that the bigger UPS will use marginally more or less power because its running at a different point in the efficiency curve - its impossible to say without knowing precise details of the unit, and its unlikely to be consequential.

That said, if you have a 6kva unit, it means that the components are rated for higher current, which means they will be more reliable. It also means you can have a higher maximum power draw from them (but this will, of-course, deplete the batteries faster)

This does, of-course, assume that the UPS's are "like-for-like", ie they are otherwise similar models.

To add to the other answers, just make sure you have the infrastructure to be able to power it.

A 6kVA UPS will need (in North America) either an L6-30R twist-lock (or L14-30, or similar - not sure what's used in India for ~30A circuits? Probably a commando type) :

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receptacle or a hardwire mains supply on a circuit with 30A capacity (for 208V-230V input).

In India, a 3kVA unit will probably just use a standard power plug (M-Plug to IEC 320 C20) - a 6kVA unit will not.