Extended vs flush chokes
Some pros and cons of extended choke tubes include:
1) extended tubes are usually easier/faster to change (usually no wrench needed),
2) most extended tubes have the choke/constriction printed on the exposed portion (visible when installed) while some flush tubes don’t have notches to indicate choke constrictions when installed,
3) extended tubes provide muzzle protection from possible muzzle damage (dint) that could make choke removal or instillation difficult,
4) extended tubes provide additional length which allows for the possibility of different choke geometry and design (ramp angle and length, choke angle and length, parallel section length, porting and endless marketing gimmicks) which may or may not provide improved performance,
5) extended tubes usually weigh more than flush tubes which may or may not be a good thing for your gun’s balance,
6) some shooters think the extended tubes look cool and some like the traditional uncluttered look of flush tubes, and
7) extended tubes are generally more expensive (the choke makers like that).
None of this means extended choke tubes work/perform "better" (whatever that means) than flush chokes. It really depends on the kind of performance you need/want from your chokes and loads for your type of hunting/shooting. However, if you aren't going to take the time to pattern them properly (with the ammo you use) to find out how they really perform then it doesn't really matter, just use what you like.
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One other thing, extended chokes add a extra inch or more to the total barrel length. That affects every aspect of the shot pattern, size and speed. Not much but it is the same argument between 30, 32 and 34 inch barrels. Powder gets the most effective pressures at a certain length, different foe each powder and load.
Like many here, I have spent a fortune on all different brands, sizes and constriction and they are all different! Carlson is a great choke but Briley is better. Personally, I like Muller competition chokes as the constriction is non standard. Almost everyone else has a .005 degree between chokes so a full is .695, light full is .700, improved mod is .705 and so forth. Muller #2 is.003 degrees less than mod and to me is perfect for regular 50 yard sporting clays.
But it always changes. Each gun likes a particular choke and a particular load in a particular hull, powder, wadd and powder. Trying a new 1 ounce load ar 1325fps and 9800 psi tomorrow. Psi translates not perceived recoil which determine flinch the more shots are fired in a day. 1 1/8 at 1150 to 1200 is a great load, especially with Hogdones International or Clay's powder. Good luck getting any!