I've always found rationalizing coil strength (its magnetic field) to be a confusing topic. The equations for coil power don't actually take wire gauge into account, but it indirectly effects the results because the resistance of the wire changes and that can alter the current, and current is part of the magnetic field equation. Which is what happens in our pinball application as we have a constant supply voltage so changing the coil resistance changes its current and thus its power.
The other things that come into play when determining the mag field:
1) The physical coil Length (like our voltage situation, all 3 coils have effectively the same length as they fit the same mechanism)
2) Permeability (again, we are not changing the plunger)
Since most of the other equation elements stay fixed in our application, it really boils down to how we change the current when we replace the coil, and that's directly related to the coils resistance. So Turns and Wire Gauge are important.
In this case, the data I've found (I looked it up, I didn't actually pull out my DMM) is that the 26-800 and the 25-1000 are roughly identical "strength" wise (have the same resistance, thus current is the same) at 7.5 ish ohms. 26 awg has a smaller radius than 25 awg and thus has higher resistance per foot. But the 25 awg coil has more turns (more feet of wire). The net result in this case seems to be more resistance and shorter = less resistance and longer.
Quoted from Deleenhe:Page 2-23 of the manual says it should be AE-23-800 and the solenoid table on page 3-5 says it is AE-26-800.
However, the 23-800 comes in at around 4.2 ohms (less turns, thicker lower resistance wire) so it's going to be a stronger coil as the amperage draw will be higher. So you can't just go by turns alone.