Yzerman's last 2 years kept him from being 2nd overall along with the fact that Howe and Messier as well as Francis played 150-200 more career games than Yzerman.
To the OP, I'm going to parrot what others have already said. Yzerman was the better Red Wing, Lidstrom the better player. That said...
I actually came here to refute this point by saying that Stevie's body broke down in later years, and he no longer would've been able to compete with a purely offensive game. I still think this is true, and I don't believe he would've lasted 12 more seasons that way.
I took a quick peek at the all time scoring leaders, and it is not unfeasible (hi, double negative!) that he could've taken the number two all time spot if things had gone differently. Had he even played one more season in the real world, he definitely would've ousted Dionne, and possibly even taken the #4 spot from Francis had he remained healthy (given his numbers from his last two seasons -- 75gp, 55p and 61gp, 34p).
With him only 132 pts behind Messier even with his switch up to two way play, I could honestly have seen him topping every other forward all time save for the Great One.
2 Mark Messier EDM, NYR, VAN, NYR 1756 1887 1.07 3 Gordie Howe DET, HFD 1767 1850 1.05 4 Ron Francis HFD, PIT, CAR, TOR 1731 1798 1.04 5 Marcel Dionne DET, LAK, NYR 1348 1771 1.31 6 Steve Yzerman DET 1514 1755 1.16
...of course then we'd have exactly zero cups, and people would be talking about how he was the best centerman never to win the big one...
Another thing, Demers was the one that turned Yzerman into a 2-way centre. Bowman took over and had the 1991 draft done and a team that got stacked with Lids, Federov, Konstantinov and then had the Grind Line and Shanny added along with Larionov and Fetisov. That team was a raging hard-on that just needed the right system. The same thing he did when he had the Penguins back to back championships with the likes of Lemieux, Jagr, Francis, Coffey, Barasso, Stevens and so on. They just needed organization to win the cup.
And I'd put Yzerman ahead of Lemieux on the all time list at centre in a heartbeat, as well as Gretzky. Centres need to be responsible on both sides and Yzerman was far superior to Lemieux and Gretzky in every way but point totals. I'd sooner put those 2 on Yzerman's wing and make a super line and have Sakic as my 2nd line centre who was the closest comparison as stated by someone else above for Stevie Y.