Just to point out, Byrne's Superman was a couple years before LODK debuted, so Byrne' Superman couldn't change something LODK was responsible for. Byrne's last Superman issue was #22 cover dated Oct '88, LODK debuted cover dated Nov '89. Did you mean DKR?

The demand for Dark Knight was greater than most retailers anticipated, hence the massive sellouts of the first issue and second issues and the second printings for both (and the second printing of #1 was an immediate sell out in a lot of shops as well). That demand carried over to the Batman and Detective series in a lot of shops as it became hard to find shelf copies for a short bit after the advent of DKR as retailers had to adjust their ordering on Batman to meet the new demand. At our shop he had a sign out for 2 months about the time DKR #3 hit that if you were adding Batman or Detective to your pull list, you might not get a copy for a month or two as he was adjusting orders to get more each month and was trying to reorder copies of the upcoming issues to meet new demand, but was going to make sure existing pull customers got their copies first before new subscribers. He also had one of his employees scouring newsstands to pick up extra copies to meet the influx of demand for recent issues of those series. I was one of the customers trying to add the books at the time (and trying to get a copy of DKR 1, and managed only to get a 2nd print of that at the time).

Man of Steel on the other hand, had plenty of copies of both covers to go around, as retailers ordered heavy on it, and many (my shop included) had a couple of cases of extras left over that were not even cracked open after the initial wave of demand subsided.

By the time LODK launched, demand for Batman was expected and shops ordered accordingly. The movie created additional demand, but shops had been riding a wave of increasing demand for Batman related material for 3 years up to that point and if they were paying attention to the trends were able to anticipate the rising demand and order to meet it.

As far as Dark Knight returns goes though, Miller was the big draw, not Batman at first. Retailers had seen the unexpected demand curve on Ronin #1 previously, and many had been caught short on that (Ronin #1 was one of those hot back issue books at the time) and Miller's Daredevil was a good seller as back issues and were getting decent prices, so a lot of the interest in DKR leading up to it was what would Miller do with Batman? That it lead to a surge in demand for Batman coming out of it was a windfall for DC. Sales were increasing on the Bat-titles on the back of DKR, but when Miller was announced to be taking over the book to do Year One starting in issue #404, interest and anticipation again surged and retailers remembering what happened with DKR upped orders significantly on those issues and it still sold better than anticipated. After Year One wrapped, sales dipped a bit on Batman, but were still higher than pre-Year One numbers (mostly I think from fewer buyers getting multiple copies than form losing regular buyers).

So the growth of demand for Batman in the mid-to late 80s happened in several stages. All the while, if you were reading Comic Buyer's Guide (and I had subscribed in late '86 and got it through '90 or '91 regularly), the letters pages and columns were abuzz and ablaze with rumors, bits of news, and discussion of the anticipated Batman movie. It started slowly after DKR, but reached a fever pitch in late '87 and through most of '88 and by '89 it seemed it was the only thing people were talking about in CBG (a bit of hyperbole based on the impressions of my memories of the time, but not much).

For all the flak Miller gets for his post-80s material, and for all the cries of his Batman stuff being over-rated or detrimental to the Batman mythos, he was one of the prime driving forces for the surge in popularity of Batman in the mid-80s and kept driving that surge through the decade. Another factor that people forget in that surge in popularity was Warner books (not DC) choosing to collect DKR into one of the early DC trades and put it into mainstream bookstores, where it became a huge seller, going through a couple of printing quickly (I think it was the second or third printing where the trade dress changed from Warner Books to DC) which not only put Batman comics in front of a whole new set of eyes and brought new customers to the game, but it also laid the groundwork for the growth of trade paperbacks as a new segment of the market. A lot of people who encountered that book in bookstores had never been to a comic shop but became interested in Batman (or interested again as most were at least familiar with the character from childhood) adding to that rising wave of demand for Batman products.

Batman was on a different trajectory than Superman was through the 80s. Some of it was the comics themselves. Some of it the characters in other media (the perception of Superman via the latter Reeves movies), some of it was the zeitgeist of the times (which was captured by Miller in DKR in the contrasts between the portrayals of Supes and Bats therein). Though they were of an age both coming from the 30s, Superman still felt like your parent's super-hero, something that was popular once but whose star had faded (despite Byrne's efforts to put a new shine on it), but Batman felt contemporary for the times.

Superman did improve in sales and had a strong run through the triangle era and the death and return), but it never had the surging trajectory of new interest Batman had in that era. And the name at the launch point of that trajectory was Frank Miller.

-M