I currently use 2 Fishers, an F5 and an F70, and have concentrics and DD's for both.
Also used an F2 for a few years and a couple thousand hours and used only concentrics on that one, did the best with a small round concentric Fisher hockey puck coil.
I have lived and hunted in areas with both fantastic dream dirt and also with high mineralized soil and in many different sites both clean and with insane amounts of iron and trash.
Honestly I am a big fan of both coil types but I usually let site and dirt conditions govern what I choose to use and since I now live in an area with highly mineralized red dirt and clay and massive iron and trash challenges DD's have the upper hand nowadays...usually.
Still pull out my concentrics though, here and there, the pure sweet tone I hear over good targets and especially high tone silver using a concentric is something I learned to notice and listen for after hundreds of hours swinging Fishers with concentric coils.
It's there, just slightly different than the sound of a DD coil over the same kind of targets and something you can pick up on with a several hours experience listening to and noticing that unique tone.
Silver especially just sings on a Fisher with a concentric coil...in my experience, anyway.
Concentrics are actually a bit deeper in good dirt although the deeper scanning areas are quite a bit smaller than the full width of a DD field at depth.
In mineralized dirt DD's do actually seem to be slightly deeper or at least seem to have a little more stable and accurate ID's but it is not a huge difference over most concentrics I have used on my Fishers.
I hunt public parks and other areas with heavy iron and crazy amounts of trash and bottle caps can be a problem but using a concentric coil not hardly all because disc is actually a bit sharper and better on concentrics vs DD's.
I can ID them about 95% of the time if not more with a concentric mounted on a Fisher by their behavior, they just won't lock on or seem stable using them.
More of an issue when you swing over these with DD coils using most every brand or they could be because so many can come in solid and sound pretty good but using the wiggle and pull back method with a DD mounted on a Fisher unit problem caps will usually drop down from high number, solid seeming dig me targets to low foil or into iron as you pass the front end of the coil over them about that same 95% of the time or more.
This technique saved me and my sanity after I learned to do this and is one of the most helpful and useful things I have learned in this hobby after I gained confidence with this technique.
As far as sizes I have used concentrics and DD's in a few different sizes on my Fishers for years including that 11" DD.
Not sure how it works on that 44 but on both the F5 and the F70 the big DD not only works great at most sites and has great separation and depth but by turning down the gain to lower levels it seems to make that bigger DD think it changed into a laser-like smaller sniper coil with excellent separation and still gets scary deep.
Don't know how or why it can do this but it just does.
All coil sizes work pretty well but since 99% of the time I hunt in very trashy site conditions smaller sniper coils have become my favorites.
I have used Fisher small round DD coils for years and have done extremely well with tons of coins and a shocking amount of jewelry added to my collections but over the years I have come to believe a Nel Sharpshooter coil, or I suppose the Cors Fortune coil which is exactly the same thing, mounted on a Fisher detector is a combination than can be hard to beat.
Shockingly deep and surprisingly stable even deep or in difficult and challenging soil vs my Fisher coils probably due to better shielding those companies seem to add to their products.
I don't feel my detectors are complete until I have a Sharpshooter coil in the arsenal for any of my Fishers and if you come across me hunting out there with a Fisher chances are that coil will be the one I have mounted.
All Fishers seem to work great, as you can tell I am a big fan of that brand and like I said I have done better than well using all kinds and sizes of coils but put a Fisher in my hands with a Sharpshooter mounted on the end of my rod and you will be looking at a very confident and happy hunter.
With your two choices knowing what I know now as the better overall I would probably opt for the 11" DD.
Or, the teardrop concentric is supposedly pretty good and you can go for that and think about getting a DD later if you think that would be prudent.
All my Fishers found me enough clad and treasure to pay for any and all of my accessories very quickly.