Popularity is not just a measure of who bought games 16 and 18 years ago. It's a measure of how well known and enjoyed the installment is. I think if you were to survey the Japanese public on their Final Fantasy knowledge, you'd find that FFIV ranks higher than FFIII despite the similar shipments.
Put it this way; FFVII and FFVIII sold comparably (within ~20% of each other, sales-wise, when all is said and done) in Japan, but FFVII is certifiably more popular. No doubt about it.
I don't personally have the time or inclination to do textual analysis of every Famitsu issue and every 2ch post and operationalize the variables and present to you a statistically valid comparison between FFIII and FFIV, but I think if one were to do this, they'd find that FFII and FFIII are probably the least popular installments of the series.