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According to https://en.wikipedia.org/wiki/Apple_IIGS the Apple IIGS, in its year of introduction, outsold the Macintosh, without being substantially cheaper than it. This is somewhat counterintuitive: one usually expects that at close to the same price, customers will tend to prefer the newer machine.
Why was the Apple IIGS so popular? Was it because of compatibility with the large portfolio of Apple II software, or some other reason?
Over most of the 80s, the whole Mac division was financed by the Apple II profits.
Your question conflates two questions into one:
Others have given valid reasons for (2), but there is evidence that the answer to (1) is "No".
For instance this source says the Mac sold a million units by 1987, which is about what the IIgs sold over its whole lifetime - according to a former manager of the Apple II division quoted by Brutal Deluxe in their project to collect IIgs serial numbers and estimate sales data.
The Mac number roughly matches Jeremy Reimer's sales data which he used to write this article, and which I used when answering "Over its lifetime, how many Apple II computers were sold?"
Scaling Brutal Deluxe's estimated sales data by the 1 million IIgs limit gives about 122,000 units in 1986-1987 (peaking at 305,000 in 1988) vs the Mac's 380,000 in 1986 alone (900,000 in 1988).
It was the Apple //e that funded development of the Mac - until around 1988 when Macs finally started to sell more than the whole Apple II line. The full data for Apple II's and Macs from my other answer is in this Google Docs Sheet, with various notes about assumptions etc.
There was a big "Apple II Forever" push encouraging users to upgrade. Also schools likely bought IIgses in bulk for their computer labs, driving up the sales figures.
There are 3 main reasons:
there was way more software, especially games, for the Apple II than for Mac at the time; also those games were often in color
it was a color computer
it was easy to program; both schools and power users loved the easy access to the Applesoft Basic interpreter on the computer; the Mac required specialized toolkits to program and a much higher skill level
The Apple IIgs was introduced in September 1986. The base machine list price was $999. At that time, a Mac Plus listed for $2600 and was a "closed" architecture. The first color Mac came out in March of 1987 and was the Mac II. The list price just for the Mac II itself was $3898 not including any peripherals (for example, it lacked any built-in internal video). The IIgs actually could be purchased by itself and used with MANY existing older peripherals making it a lot more cost effective (one did not need to add a video card or a floppy controller as they were built in). Not only that, the Apple IIgs had an emulation mode that allowed it to work with 90% of existing Apple II software dating back to the Apple II's inception in 1977. Combine these factors and you have a winner at that time. It took until October 1990 for Apple to release a "low cost" color Mac.
The 8bit guy did a YouTube video about Steve Job's biggest mistakes. It was a very well done video about comparing the Macintosh vs the AppleIIGS ... and the summary was that in almost every respect the AppleIIGS was a superior machine (in terms of both performance and cost). And that the Macintosh was Steve Jobs attempt to gain more footing at Apple.
