Back when that episode was made (and a subsequent King of The Hill episode, too), the transition towards lower water usage wasn't being accompanied by very smart engineering. So the flushes of the original 1.6 gallon-per-flush toilets were pretty bad. Didn't evacuate much mass from the bowl and didn't work reliably. We had a beautiful Kohler toilet from that era. Expensive. Very nice-looking. I swear if you put much more than one sheet of toilet paper in it, it clogged. And the design was so bad that adding water to the flush, holding down the handle, didn't help one bit. I eventually replaced it with a Toto Drake, one of the earlier high-performance low-flows, and never looked back. That toilet works wonderfully.
For a long time, we were advocating almost entirely Totos on this forum, because across the model line, they flushed very will and were very-consistently-made, with high quality-control, so when you got it home, it had zero defects. (Japanese company, so it's made like a Toyota, meaning well and consistently). They still flush as well or better than any brand, but some other manufacturers are finally starting to catch up on performance, and starting to realize that quality means something.
A friend of mine recently put a $99 Glacier Bay 1.28 gallon-per-flush toilet in the mens room at her bar (which is a colorful place where things get broken). I don't think the fill valve was ready for prime time, but the contractor replaced it with a Fluidmaster 400A. The thing ran fine, with virtually no clogs despite some real abuse, until someone smashed the tank about 2 months ago. Replaced it with another $99 Glacier Bay. Because a cheapo brand like that is often changing models, the tank from the new one didn't fit the old one, so the whole thing had to be replaced, but the new one (also with a cheapo fill valve that isn't likely up to frequent commercial use) has flushed everything thrown at it for several weeks. But putting in a good valve costs maybe $14, so no big deal.
The new flushes aren't "manly" like Al Bundy's preferred flush. It's more like "slurp, gurgle...gone". The science of the flushes is not that the bowl fills with water and pushes the waste down. It's that a siphon is created using very little water, which sucks (slurp) the waste from the bowl. Very anticlimactic, but very effective.
We can recommend the Toto Drake (CST744E), Toto Drake II (CST454CEFG), and even the Toto Entrada (CST244EF), as well as the more-expensive Totos. The Entrada is a Best Buy, very-reasonably-priced yet very well made, with a very-very-effective flush. The street price (from a good plumbing supply place or other good sources when you do your research) is substantially-less than list price on these toilets (even less than Home Depot charges for them on special order), so they are worth looking at.
If you want a very-exciting flush that offers a real WOOSH!!!, then look at a pressure-assist toilet, with the Sloan Flushmate (the other pressure flush units are less-reliable than the Sloan and should be avoided). It uses the same amount of water as the efficient gravity-flush toilets, but is much more dramatic. And it flushes well. Gerber and American Standard make some good pressure-assist models.
I shy away from Kohler, because they made that horrible, expensive, badly-performing low-flow that tortured me for years and marketed it as if it were a great toilet, when they had to know how badly it sucked. Between the toilet and the plumber's markup on it and the plumber's expensive price to "set" it (a Long Island thing), we probably spent over a thousand dollars on it. And I will never forgive them for that. Particularly after I was able to replace it myself with a fantastic Toto for less than $250. No more Kohler in our house ever. There are plenty of other manufacturers who didn't gleefully inflict garbage on their customers for years.