The two are very different in flavor and mechanics. They really don't have much in common.
The Iron Kingdoms is a very grim n' gritty setting. It has a strong steampunk vibe both in trappings and themes, although Privateer Press for some reason dislikes the term steampunk, preferring Full Metal Fantasy. It pays lip service to standard D&D, but doesn't bend over backwards to include it; it's about as close to Greyhawk as Dark Sun is. The mecha, which are the only real connection to Dragonmech, are lumbering, steampowered uber-golems. Despite appearing on the cover of the Character Guide, they're not really meant for PC use and play a much bigger role in the attached wargame, Warmachine Prime.
Dragonmech is both more sci-fi and a more D&D. I'm not as familiar with the line, but from what I've seen it's built around the mecha from the ground up, and they are integral to the way the PCs interact with the world. The mecha are integrated across the board - everything from dwarves to orcs to aboleths(!) gets its own variety. Mecha aside, the setting is an interesting twist on the classic dragon invasion plotline and I suppose you could run a fun campaign even if the PCs never hopped in a 100-ft. tall magical machine.
Dragonmech is more modular and a vastly better resource. You could rip the mecha from it and use them in another setting - Eberron would be appropriate. Certainly the monsters could be used anywhere. The crunch is much better than the Iron Kingdoms'. It's a great d20 resource and a good setting.
The Iron Kingdoms is more complete as a setting. It has 400 pages of pure fluff dedicated to its intricately detailed setting, a huge character guide, three critically acclaimed modules and arguably the best monster book on the market from a flavor perspective. The crunch is weak if not indecipherable, the fluff is suberb, and it's a worthy successor to the great settings of 2e.