Data point - I tried the Finish Powerball and I must say I’m impressed. The dishes are much cleaner than they were with the generic gel I was previously using. At about 14 cents a tab, they are similar in cost to the name-brand powders and gels.
In our house, fella bilong missus flodnak loads and starts the dishwasher. If it were me, I’d go with the powder, because I’m a cheapskate like that, but he loves the tablets. His advice is to go with the ones you have to unwrap rather than the ones with the self-dissolving film, because if the film doesn’t dissolve entirely, it makes an incredible mess.
It costs more than using the powder would, but it is worth it to keep peace in the kitchen 
I like them. They do a heck of a job cleaning, and they leave no residue. I’m sure they would be more expensive, if I were to buy them a box at at time. Our local supermarket usually puts them on a “buy one get one” sale every other month. If you couple that with the coupons in the Sunday paper (which get doubled), you end up with a two month supply for about a buck.
When I got my new dishwasher, the installer told me to use those things, but only half (according to him, a whole one was too much soap) and to use a separate rinsing agent.
When I’ve followed his instructions, my dishes have come out cleaner than when I haven’t.
I also love the Purex 3-in-one, but I can’t find them around here for some reason.
If you have a front-loading, HE washer, be careful about these. I used them almost exclusively for about a year and a half, and recently had to have my washer repaired. (I only stopped using them because they got hard to find around here, too). A little online research backs up what the repair guy told me: some of the ‘fuzz’ and waxy coating from them will stop up the drain hose, causing the machine to drain incorrectly. This leads to an ‘ERROR’ message, and having to re-start the washer a number of times. Eventually, the front had to be taken off the machine and the drain hose cleaned out, which was very messy and cost me $30.00 in repair time! I’m all liquid from now on!
BTW, sorry for the hijack!