Let's step backwards a bit and answer some "unasked" questions first:
- What is a color profile.
- What is a "monitor" profile and hardware calibration vs a "Factory Profile."
- What is color constancy.
(I will make the assumption that the OP has not calibrated his monitors using "expert mode" nor a hardware calibrator.)
WHAT IS A PROFILE
ICC profiles are just a description of a way to transform color data. Put another way it describes how, within the ICC system, a specific color value should appear. For instance the hex color value
#00FF00 means maximum green. But just how maximum? Maximum green is DIFFERENT depending on the color space. ICC profiles are the "treasure map" for where to find what such-and-such a color value relates to in terms of appearance.
Here's an example: The first patch is hex
#00BD00 in sRGB, the other patches show what the hex value
#00BD00 looks like when you send that number WITHOUT CONVERSION to those three other colorspaces:
Put another way,
#00BD00 in Rec2020 looks like
#00CF00 in sRGB, and
#00BD00 in ProPhoto looks like
#00DD00 in sRGB.
ICC profiles and color management take a particular VALUE as it RELATES to a particular COLOR SPACE and then coverts the value to what it needs to be in a DESTINATION color space.
WHAT IS A MONITOR PROFILE AND CALIBRATION
A Monitor Profile is a profile that ideally is based on the actual measurements of the color properties of a particular monitor. The idea than is the color management software knows how a value of
#123456 should appear on that monitor, relative to some reference color space.
Hardware Calibration means the monitor's controls have been adjusted to a particular specification with the help of a colorimeter such as an X-Rite i1 DisplayPro.
Hardware Profiling means that the colorimeter and software has created a profile specific to that particular monitor.
A Factory Profile is typically a generic profile based on a brand-new version of a particular monitor model. The profile is likely made on a prototype under laboratory conditions. The chances it actually matches a particular monitor are somewhere between "slim" and "LOL NOT."
WHAT IS COLOR CONSTANCY
Human visual perception is not even remotely uniform. It is relative, and non-linear. Perception of a particular color is highly dependent on the surrounding colors and environment.
See this well known optical illusion:
The hex values for BOTH square A and B are
#6F6F6F, yet A is perceived as much darker than B due to the relative surrounding image.
This applies to monitors in a big way. Two different brands side by side will rarely match. But either one in isolation will probably look correct.
(Nevertheless, one with a significant color or gamma error will likely end up causing images edited on it to end up a bit off.)
How This Applies to the Question
OP has a few things going on:
- A MacBook with a glossy screen that is using Apple's factory calibration.
- An old ASUS monitor which probably has a matte screen and has not been calibrated nor profiled using a colorimeter.
- A factory profile for the ASUS that is probably irrelevant.
- Ambient light that could be incandescent? (3200K).
Color constancy causes the appearance of one monitor to affect the perception of the other monitor.
The monitors are unlikely to match. The monitor with the matte screen will also be affected by ambient light differently than the gloss MacBook screen, and if incandescent lighting is used may appear more orange or brown.
MacBook glossy screens tend to lean toward blueish. Also, they can be perceptually more contrasty than matte screens.
Both screens are of a different age/operating hours. LCDs shift yellowish with age.
The sRGB generic profile is essentially a "straight through" profile, sending values to the external monitor "essentially unchanged" if you are working in a sRGB space.
As it happens I am typing this on a 2013 MacBookPro.
What profile is selected for your laptop screen? "Color LCD" (i.e. the standard that ships with the laptop)? If you look at the curves in that profile you will see they are all three fairly different, especially the blue.
If you use EXPERT mode to calibrate/profile the MacBook, the resultant curves will be WAY different (and far from uniform). Here's the blue curve from the last time I did an "expert mode" non-hardware calibration of this laptop:
This calibration/profile was in the room light I normally use. I do have hardware colorimeters, but for MacBooks with glossy screens they don't seem to work particularly well.
As such, in your case it would appear that sending plain sRGB out to your monitor is closer in tone to your current MacBook.
You might try using expert mode to profile both monitors. TO access it, in system preferences select Displays -> Color, and then hold down option while selecting "calibrate".
You can also look at your profiles in Displays -> Color by clicking Open Profile, and taking a look at the resultant curves.