Plug aeration works best for our type of soil. Below is a link to the plug aerator that I use. I am very satisfied with it.

Lowes's Plug Aerator

-Deerslayer

What do you mean "our type of soil"? Are you referring to the midwest or you in particular?

Based upon my own experience over-seeding a couple of times, the plug aerator has done a great job for that. The holes plus the plugs of soil kicked up as you go provide an ideal medium for grass seeds to be broadcast followed by starter fertilizer. I would do this as soon as we get past the sustained hot weather so you can keep the seeds irrigated.
I have never tried the tine model for over-seeding, but my guess is that it would not be quite as suited to the task of over-seeding since it does not work up nearly as much soil.

Here is a link that might be useful: Brinly Aerator from Home Depot

"Are you referring to the midwest or you in particular?"

Zone 5A in Illinois and Wisconsin. I'm assuming that you do not have sandy soil. You cannot pull plugs in sandy soil.

-Deerslayer

An aerator won't fix "dying grass caused by excessive irrigation".

You may not need to aerate at all once you fix the water problem.

If you are going to buy one, get it now. When I tried to buy 3 yrs ago, I made the mistake of waiting until the end of Aug. I could not find one in stock anywhere around here. I ended up borrowing one from a friend across town. I bought one the next July and haven't looked back. I bought the 40" Craftsman. It was bit more expensive than the home centers, but seemed heavier duty. It has performed flawlessly for the last 2 years on my lawn, my neighbors and a couple of family members.

Here is a link that might be useful: Craftsman 40

I may have a fungus and one of the suggested solutions, besides stop watering, is to aerate the soil.

I took my chances with this "heavy duty" plug aerator. Some people loved it and some hated it. But it worked for me with my crap soil and rock. My grass thickened right up this year. I am very happy with it.

Here is a link that might be useful: Sears 42

Deerslayer,
Actually you can pull plugs in sandy soil. It just has to be a little wet, like a day or two (at most) after a heavy rain.
I started out with the Argi-fab spike aerator/spreader and hated it. It wasn't heavy enough to dig in and really aerate the soil (even in sand). The only thing I could see it being useful for is seeding tilled soil. I took it back after one use and bought a Brinly plug aerator, which I weigh down with two cinder blocks, filled with concrete and rebar handles. That probably puts about 140lbs on it, which allow it to pull up 1.5-2" plugs. If I were overseeding, I'd aerate first, then go over it with my broadcast spreader. That's what I do when I put down 700-1000lbs of lime (depending on the ph tests) each spring. I don't really see the point in having one implement which does two jobs poorly (unless you're really strapped for storage space), instead of two pieces that each do their own job very well. A spike aerator alone would probably work fine with a weight shelf, but the combination hopper/aerator doesn't allow you to weigh it down.
An aerator is an incredibly good purchase for a lawn tractor. When you consider renting a professional walk-behind plug aerator is around $100, it pretty much pays for itself after two uses.
Also, a good plug aerator with a lot of weight on it can really tear things up (if you want it to). Before I had my tiller, I had to regrade a small portion of my front lawn before reseeding it. After a dozen or so passes with the aerator, it looked like I'd tilled it.

"Actually you can pull plugs in sandy soil. It just has to be a little wet, like a day or two (at most) after a heavy rain."

I suppose it depends on what you mean by sandy. I lived near New Orleans for awhile and the soil was basically sand. I've seen the same type of soil in parts of Florida. I would be surprised if plugs could be pulled from those locations even after a rain but I suppose anything is possible.

In any case, I've read at several websites that core aeration works better in clay soils and spike aeration works better in sandy soils. Here's a link to one.

Aeration

-Deerslayer

Deerslayer,
That's a good link, but note that the author has clay soil and uses a plug aerator. It seems his recommendations that a spike aerator works better in sand are just speculation. My soil is 90-95% sand (based on a soil test I did a few years ago). And having owned both types, I'm still convinced that plug aerators work best in any type of soil. Of course you won't pull up puppy-turd-like plugs as you will in clay, but like I said, when the sand is moist, you'll definitely pull up plugs--akin to goose turds maybe? It doesn't work at all when the sand is dry; just tears up your lawn.
When you think about it, a spike aerator doesn't really do anything but poke holes for water to reach the roots, which quickly close up and leave the soil as compacted as it was in the first place. A plug aerator actually pulls up a section of soil, which then spreads out on the surface, reducing the overall density of the soil while it bores holes for water to reach the roots. I just think a plug aerator is the way to go no matter where you are.

On a side note, a good soil composition test I read about one time is to fill up a large jar 2/3 full with soil from your yard, fill it to the rim with water, then put in a little dishwashing soap to act as a surfactant (did I spell that right?). Shake it up and let it settle. The sand will settle first (make a mark with a sharpie), then the clay, and last the loam. I think the whole process took about 8 hours.

"It seems his recommendations that a spike aerator works better in sand are just speculation."

I think that it is more than speculation. I've seen the same assertion made in several articles. From the article above:

"Current opinion is that hollow tines, which remove plugs of turf, roots, and soil, are best used to aerate compacted clay soils. Solid, spikelike tines that poke holes in the turf but don't remove plugs are best used to aerate sandy soils."

Here's a link to a GardenWeb Lawn Care FAQ.

Spike or Core Aeration

If you think that core aeration works better in your case, great, go for it.

-Deerslayer