What is the difference between the two in terms of affecting signal strength or performance? Where I work, everything is on channel 1 6 and 11 for the 2.4GHz spectrum and I've been told that co-channel interference is more manageable or better than adjacent channel interference. Why is this? Wouldn't the lack of separation between each one make it worse?
It's a question of what kind of noise you want to deal with - in general adjacent channel noise is easier to deal with than co-channel noise (frequency congestion).
To illustrate I've cribbed the images below from the Chanalyzer User Guide - I will give them a plug by saying that an appropriate spectrum analyzer is critical when setting up WiFi in high-density environments, and their tool is the one I've used in the past.
Adjacent channel noise occurs because no RF transmitter is perfectly "on frequency" - there is a bandwidth used by the transmitter, and a tolerance band around each channel.
By looking at a spectrum analyzer you can determine which available channels are "cleanest", and then assign them to your access points, taking into account RF bleed-over to ensure that your access points don't (substantially) interfere with each other - this is what your colleagues are referring to when they talk about "managing adjacent channel noise".
If you mess up and have access points too close together they essentially get into a shouting match to see who controls the frequency at any given time. The image below shows two access points on what appear to be channels 10 and either 11 or 12 (notice how their peaks are right on top of each other).
Co-Channel noise is a bit different, and not easily illustrated on a spectrum analyzer.
In each room there is a resident guru dispensing wisdom (the AP).
Carrying our hotel analogy further, as people start shouting you can hear them in the next room - this is adjacent channel interference (bleed-over), and as shown above the way to deal with it is not to fully book your hotel, so there are a few "empty rooms" between each group of shouters.
So to directly answer the question you asked:
In terms of performance, both are Bad Things.
In terms of signal strength, remember that your "signal strength" bars on your laptop are not just "strength" - they show a combination of signal strength (dBmV) and signal-to-noise ratio.
Adjacent channel interference may show a lower "signal strength" because of the noise from the adjacent channels bleeding over, but the overall performance on a 2-3 bar signal may be better because there's less competition to talk to the access point.
Note that the solution to each type of interference of necessity creates the other: