Just a quick comparison
Xiaomi Redmi note 3: Credits Gsmarena
Acer Liquid Z630s: credits: Gsmarena
The link speeds you mentioned are usually achieved only under ideal conditions which is not usually the case in situations where there is a lot of wave interference from other devices.
Additionally, the maximum speeds you see may depend on the wireless standard supported by the devices. I this case we see that the Acer Liquid Z630s supports Wi-Fi
802.11 b/g/n, while Xiaomi Redmi note 3 supports Wi-Fi
802.11 a/b/g/n/ac, as well as dual-band.
Brief history of Wireless standards
802.11b: This was the first commercialized wireless standard. It offers a top speed of 11 Mbps and operates only on the 2.4 GHz
frequency band. The standard was first available in 1999 and is now
totally obsolete; 802.11b clients, however, are still supported by
access points of later Wi-Fi standards.
802.11a: Similar to 802.11b in terms of age, 802.11a offers a speed cap of 54 Mbps at the expense of much shorter range, and uses
the 5 GHz band. It's also now obsolete, though it's still supported by
new access points for backward compatibility.
802.11g: Introduced in 2003, the 802.11g standard marked the first time wireless networking was called Wi-Fi. The standard offers the top
speed of 54 Mbps but operates on the 2.4 GHz band, hence permitting
better range than the 802.11a standard. It's used by many older mobile
devices, such as the iPhone 3G and the iPhone 3Gs . This standard is
supported by access points of later standards. 802.11g is also
802.11n or Wireless-N: Available since 2009, 802.11n has been the most popular Wi-Fi standard, with lots of improvements over the
previous ones, such as making the range of the 5 GHz band more
comparable to that of the 2.4 GHz band. The standard operates on both
2.4 GHz and 5 GHz bands and started a new era of dual-band routers, which accommodate two access points, one for each band.
802.11ac: Sometimes referred to as 5G Wi-Fi, this latest Wi-Fi standard operates only on the 5 GHz frequency band and currently
offers Wi-Fi speeds of up to 2,167 Mbps (or even faster with latest
chip) when used in the quad-stream (4x4) setup. The standard also
comes with the 3x3, 2x2, 1x1 setups that cap at 1,300 Mbps, 900 Mbps
and 450 Mbps, respectively.
Comparison between the bands
The 2.4 GHz band is a pretty crowded place, because it’s used by more than just Wi-Fi. Old cordless phones, garage door openers, baby monitors, and other devices tend to use the 2.4 GHz band. The longer waves used by the 2.4 GHz band are better suited to longer ranges and transmission through walls and solid objects. However, because so many devices use the 2.4 GHz band, the resulting congestion can cause dropped connections and slower-than-expected speeds.
The 5 GHz band is much less congested, which means you will likely get more stable connections. You’ll also see higher speeds. On the other hand, the shorter waves used by the 5 GHz band makes it less able to penetrate walls and solid objects.
One thing worth mentioning is that a Wi-Fi connection takes place on just one band at a time. If you have a dual-band capable client (e.g your Xiaomi device) with a dual-band router, the two will connect on just one band, likely the 5 Ghz.
As a rule of thumb: The speed of a single network connection (one pair) is determined by the slowest speed of any of the parties involved. That means if you use an 802.11ac router with an 802.11a client, the connection will cap at 54 Mbps. In order to get the top 802.11ac speed, you will need to use a device that's also 802.11ac-capable.
Troubleshooting the issue
Having gained this bit of background, we can see there are factors which may affect the speed of connection :
Since you mention that the Xiaomi device cant use 5Ghz band, its most likely it is restricted to bands which much lower speed using ealier technology.
The congestion in the 2.4Ghz band may actually slower the connection as explained above.
Your actual router may not support the latest band offering such higher speeds which may be the limiting factor, causing your device not to utilize its dual band capabilities.
Also, transmit power, receive sensitivity, and antenna layout varies between the brands and models, and can have impact on overall speed output.
Another thing I suspect (looking at the chart), it seems your Xiaomi device will be restricted to use the
a/b/g channels while the Acer device can utilise all the
b/g/n which achieve higher speeds as the 5ghz on
n channel is un-utilisable. (Note this is my reasoning and may not be conclusive)
If your Xiaomi device was made not to utilise the shorter waves which are faster, sadly there is nothing much you can do than buying a device supporting larger wide of wavelengths.
You may salvage a speed increase by opting for a router with latest standards matching the device.
What’s the Difference Between 2.4 and 5-Ghz Wi-Fi (and Which Should I Use)?
Home networking: Everything you need to know
WiFi standards explained: what you should know about the new 802.11 ad, ah & af standards
- Why does same wifi gives different speed for different devices?