DangerDude,
I have the F2, F5, F70 and others.
On my F2 I added the 4" coil and the 10" coil. With the 10" coil, it added a couple of inches of depth in air tests. But it changed the balance of the detector, I felt like I was swinging a lead weight on the end of it. I assume the 11" DD is heavier than the 10" round. The 11" coil costs much more than the 10", maybe it works that much better and would be worth the investment. Is the F2 the last metal detector you'll ever buy? I've bought several used detectors off ebay and saved a boatload of money over new. If not ebay, several online stores have used detectors, I got my F5 used for $300 instead of today's new $550.
If I had it to do over again, I wouldn't have spent the money trying to make the F2 work a little better but still short of my F5 or F70/F75. The F2 is a lower frequency and you cannot adjust the ground balance or threshold. Of course, I guess all of us would like to keep our favorite detector and have the money back on most of the rest. The F2 is the latest detector I bought, I wanted something to carry all the time at work.
With that said, I have no guesses as to why the 250 is noticeable deeper. Don't laugh, but did you turn up the sensitivity on the F2 after turning it on? It isn't at full gain when you turn it on, and does not remember your settings when you turn it off. My F2 doesn't like the dew and wet grass, sometimes it will stream a series of beeps fast and random VDIs, like 10 or so in 3 or 4 seconds when it takes off on it's own.
Maybe ask a dealer what he sees on an F2 between the 8" and 11" coils? You're right, the 11" coil is a lot of money. For how many inches more?