Played add-a-balls almost exclusively, on location back in the day in NY state. I wasn't even aware of replay games for quite some time, until my friend came home from a family vacation in NJ and told us about games he played that you could win free games on. We thought that was awesome, but to this day, I'm still an AAB fan myself.
Hard to say what my personal favorite one is, but "Gold Strike" was probably the most popular one at our local arcade. I played my very first one at another arcade, and thought it was the greatest game ever. Upon returning to our local haunt that day, I told the owner about "Gold Strike".
He got one probably within a week, and kids lined up to play it when it came in. The owner soon developed a dislike for the game, because it was such a patsy for us that very often, a 25c investment would provide an hour or more of pinball fun, punctuated frequently by the game's distinctive "thwack".
He tried often and unsuccessfully to have his mechanic tame it, eventually changing it to three balls per game. No one wanted to play it at all then, and so he relented, and put it back on five balls.
I've owned several of them over the years, and know several ways of "taming" the game, although I've never actually implemented any alterations to one.
So, in no particular order, I'll name some additional add-a-balls (all Gottlieb wedgeheads) that I would name as the top five.
"Free Fall"
"Dimension"
"Diamond Jack"
"Subway"
Gosh, now several others are coming to mind that I could easily include in the list.
"Card Trix"
"Pro Pool"
"Cow Poke"
"Melody"
"Mini Pool"
"Pin-Up"
"Lucky Hand"
"Pop A Card"
"Neptune"
Heck, there's so many great ones, I couldn't possibly name a favorite.
I'd be remiss if I failed to honorably mention a game I played more than any other at the arcade, and it isn't a Gottlieb. It's often razzed for its looks, but it's a heck of a good player; Williams "Granada".

"Palace Guard" is the AAB, and yes, it's a good player as well.
Forgot to mention "Hurdy Gurdy" above as another really good one.
Looking back, our local arcade was a wedgehead add-a-ball nirvana.
One that no one bothered with very much was "Stock Car". Not a good player at all.
There were several good Williams ones as well, including "Blast Off" and "Lucky Ace". One Bally AAB that I remember from that time was "Expressway".
For some reason, I don't recall ever playing any of the Gottlieb "flipper series" games on location, and never a "Square Head", or "Flipper Pool". They're all great games too.

"Bank Shot" and "Ship Ahoy" were the first two of the deep cabinet add-a-ball wedgeheads to appear in our local arcade. We were a little disillusioned with them, because of the modified add-a-ball design which seemed to be much stingier awarding extra balls. I don't remember if "Bank Shot" did, but the WOW on "Ship Ahoy" resets after one free ball is awarded. Maybe Gottlieb got a lot of feedback from operators who felt "Gold Strike" was too easy to beat. I know that the guy who owned our arcade thought so. Of course, we loved those marathon games back then.

In Iowa? Are you finding them locally, or getting them shipped in from other areas?

Yes, it's an add-a-ball, and a good player. Several of the Williams reverse wedgeheads were add-a-balls, and they are all fun games.
Only "Wing Ding" had a replay counterpart ("Zig-Zag").

We had a "Star Action" at the arcade. Same game, but no replay unit, white base color cabinet, and 10X the score values on the playfield.
Maybe a Bally expert can weigh in about "Expressway". I think the one we had at the arcade was an add-a-ball. Possibly some kind of conversion kit.
We also had a Gottlieb "Top Card" which was rigged to award extra balls via the replay counter. If you got the "Special" on early in the game, you could really
keep it going for a very long time, because the "Special" stays lit for the entire game. I had a game on it once that lasted about an hour and a half IIRC. I believe
it was the highest score ever on that game during it's time at that arcade. Something like 1,700,000+ (rolled it 17 times). We used to put a piece of masking tape with our name, high score and the date on the backglass replacing the previous one. It was a blast to surpass that previous high game especially when you first saw it posted and it seemed so out of reach!

Got a "Smarty" years ago for $20. It was pretty decent, except the cabinet paint was badly flaking.
I passed it on to my brother who shopped it and did a quick repaint on it, and sold it at the Allentown show for a handsome profit.

"Dimension" is a great game, but can really bite you in the butt sometimes.
You can win a lot of extra balls on it, but you can lose them very quickly too.
"Astro" is another really fun add-a-ball game which I neglected to mention.

For some reason, "Melody" seems to have great appeal to the fairer sex.

I don't believe that's an add-a-ball machine.

Thank you for posting that photo. I do recall our arcade's "Expressway" having that light on the card tray to indicate an extra ball. Replays were strictly forbidden at that time in NY, and I never ever once recall any machine anywhere which awarded a credit or replay for making the "Special". Maybe not your classic add-a-ball mode, but the feature was similar to the multi-player games which gave one free ball per ball in play (same player shoots again).

Italian export version of "Bank Shot". Are there any major differences?
I have the backglass for it, but that's it.

Would love to find one of those. The playfield artwork is sensational. Have had a couple of chances at the replay model, but passed. "Hay Ride" is the one I'd love to find.

Bally "Hi-Deal" also has "balls to play" (count down/up when extra balls are won). This game is unique in that it can play as a true add-a-ball and award replays simultaneously. One of the best Ballys ever.

I love mine. Just like "Subway" in game play. The animation is different, of course, and it has the shallow cabinet. Love the "bounce back" maneuver which can be executed on this game when the ball drains down the left outlane.

Brutal is the word!

Many years ago, I acquired a similar condition "Flip a Card" in central NJ. The backglass was nearly perfect, but the rest of the game was rough. Spent quite a bit of time on it, and got it looking and playing great. I ended up selling it to the Silverball Museum. It was there for a while, and my friends who visited there said it was one of the best playing EMs in the place. It hasn't been there for years though. I don't know if it was moved to the Florida location or what.
It's a great player, and I really enjoyed it while I had it.
Really love "Card Trix" too.

You have an export model (made for Italy).