**Short Answer**

 1. Devices mentioned have different battery capacities. They are *meant* to be charged with different *rated* current and therefore different power ( Asus device is 3950 mAh, Nobis is 2500 mAh, Droid Mini 2130 mAh capacity). 

2. OEM proprietary charging methodology  can also significantly vary current. For instance, Note 2 charging current is 1600 mAh while Xperia charging current is around 600 mAh for similar size battery

 2. You *can* force higher current for faster charging but not advisable (unless OEM offers a way)

 3. What you can do to ensure *rated* current is delivered is covered

**Long Answer**

I do not know how you are measuring power in watts directly , but power is given by this equation (ignoring power factor or efficiency of charging)

`P (Watts) = Voltage (Volts) x Current (Amps) (or corresponding milli units)`

> Reasons for difference in power drawn

Voltage supplied by a standard USB wall charger is 5V. That leaves us only current to be varied to obtain varying power

1. Typically, current drawn by the charger is dependent on 

a) **Charging Rate** Charging rate is a measure that governs at what current a battery is charged and discharged. At 1C, a battery rated 1,000mAh charges at a current of 1,000mAh. In an ideal world the battery would be fully charged in 60 minutes. At 1C, the same battery discharges at 1,000mA. Ideal charging rate is accepted to be around 0.5 to ,0.8 C for maximum battery life (battery life is measured in discharge cycles). This rate is decided by the OEM and coded in the charging algorithm implanted on ROM and varies


b)  **Battery Capacity (mAh)** or size as commonly referred. Charging rate is varied dependent on this by OEM. Battery capacity of your Asus device is 3950 mAh, Nobis is 2500 mAh, Droid Mini 2130 mAh 

c) **Battery Type**  Not really relevant since most mobile devices and tablets use Li-Ion or Li-Po batteries

2.  **Li-Ion or Li-Po charging** When you charge a battery at charging rate decided by OEM, it goes through four stages of charging (Constant Current Charge,Saturation Charge and Ready No Current and Ready), see Figure 1 of [BU-409 Charging Li-Ion](http://batteryuniversity.com/learn/article/charging_lithium_ion_batteries). As you can see from graph voltage and current vary so if you are measuring current using an app like [Ampere](https://play.google.com/store/apps/details?id=com.gombosdev.ampere) and derive wattage from current reading, ***you could end up in wrong comparison*** if you are not measuring in the same stage of charging

3.  OEM proprietary charging methodology can also significantly vary current. For instance, Note 2 charging current is 1600 mAh while Xperia charging current is around 600 mAh for similar size battery

**You are comparing  Power between Asus (3950 mAh), Nobis (2500 mAh), Droid Mini (2130 mAh), which by itself is not an apple to apple comparison and in conjunction with factors above**

Droid and Asus power drawn is similar owing to capacity of battery being similar, whereas Nobis capacity is nearly double compared to Droid,so it seems fine and there is no need to "force" more current to be drawn. Doing so will result in poor battery performance. Simply put, **forcing the battery to charge faster by increasing the current will result in a battery that discharges faster**.  This is covered in my [answer](http://android.stackexchange.com/questions/129436/how-does-charging-battery-in-normal-speed-and-trickle-affect-battery-life) and in the Battery University link above


However, to answer your question


> How do I increase power drawn?

1. Using apps from play store which claim to charge faster

2. Using "fast chargers"

3.  By flashing a kernel which permit you to alter charging current, if your device is rooted

** I do not recommend options 1 and 2 for reasons mentioned in my [answer](http://android.stackexchange.com/a/129442/131553). Option 3 is safer by comparison but needs to be cautiously tweaked and you need to understand the risks.

> How to ensure getting maximum (rated) current

1. Don't use power intensive apps  while charging. [Reasons](http://android.stackexchange.com/a/131169/131553)

2. Get the right combination of chargers and charging cables by measuring current with Ampere or [3C Battery Monitor Widget](https://play.google.com/store/apps/details?id=ccc71.bmw) to rule out charger cable problems resulting in low charging current.

3. If you are replacing charger cable, go in for a shorter thicker cable (24/ 28 awg) rather than longer, thinner cables as the former offer less resistance to current

4. Cleaning the charging port of your device by blow drying it to dislodge lint or dirt that does accumulate when your phone is in pocket or outdoor usage (they cause poor connection and increase resistance )