I have a community with great knowledge but limited resources so bows are preferenced over guns. Is there any reason why their warriors would carry "English" long bows instead of modern style compound bows? Mainly looking for tactical excuses.
Easier to use
Average user can shoot further
More accurate without practice
Smaller & lighter
Complex & slow construction
Suffers wear & tear faster
Suffers from the environment faster
Requires laminate wood, fiberglass, or carbon fiber to take full advantage
Though few consider it, the pullies can be jammed (think "mud")
Though few consider it, natural wood arrows are often too soft for the power behind the bow.
Easy to manufacture
Easy to maintain
Effective without lamination/fiberglass/carbon fiber
Highly effective with natural wood arrows
Withstands weather well
Has no moving parts to get gummed up
Longer training curve
Warranties for compound bows do not cover "dry loosing", and it's not unusual for numerous parts, especially the limbs and riser, to be damaged or destroyed after even a single dry loosing. If a string or cable breaks when the bow has been drawn this will have a similar damaging effect on the limbs.
If a string breaks on your longbow you can string it back up in seconds, with the several dry strings you carry. No doubt archers in wars over the millennia with non-technologically advanced bows did this all the time. If you break a string in similar circumstances on a compound bow you will be very lucky to be able to repair it in the field. At best a hunting trip cut short. At worst you will shortly be parrying sword strokes with your worthless bow. The broken string and destroyed bow is one example - compound bows are full of other fiddly parts like (several) pulley wheels with ballbearings which can get grit lodged in them and render the bow useless. Longbows are much simpler and more robust.
The most obvious reason is the ease of manufacture. With the right wood and a knife, you can whittle a bow. Building a compound bow requires metal working tools.
If a community has limited resources, it may not have the tools to build a compound bow.
If a community had the tools to build a compound bow, they would build crossbows instead. They are easier to use and don't require the training and practice of a bow to be proficient.
The most obvious tactical reasons to use a bow over a gun is that a bow is mostly silent and you have a chance to recover and reuse your arrows. If push came to shove, you could even make your own crude arrows if you ran out.
You said so yourself: They have limited resources. Even though compound bows are not thought for warfare, but rather for competition or, at best, hunting, they are still far superior to longbows in terms of raw power. However, they are not only harder to manufacture: they're more expensive too. If you're already making a compound bow, you're short from a gun almost just by the powder, and it isn't really justifiable over even a crossbow - which is much more low-cost in terms of maintenance and can be used with much less training - either. A longbow is a logical choice only if you need something that balances fire-power and resource usage.
I'm actually going to look at three basic possible kinds of bow, longbows, composites (made from laminated layers of materials with different compressive properties), and compounds made from modern composite materials like carbon fibre or Fiberglas.
Rate and cost of manufacture, as people have mentioned composite or compound bows are expensive and time consuming to make, if you leave a composite bow to cure by itself, rather than using an oven to force-dry the glues, then it takes years to be usable. Modern compounds just can't be manufactured below a certain limit you can't make the material let alone the finished object.
Hot climate, in a dry climate old-school bone/horn, wood, and sinew composite bows can last a lifetime, they usually don't but they can, but they tend to de-laminate when exposed to damp air for extended periods, compounds are the opposite, the sun is NOT your friend if you have a modern compound bow the resins and artificial fibres they are constructed from degrade when exposed to UV. Longbows don't suffer from either of these issues, they're a good all weather weapon.
Ease of use and efficiency of fire, compound and composite bows are only superior for horse archery; you need more room to fire either one in an infantry formation than with Longbows, not a lot more with composites (quite a bit more for compounds) but when it comes to stopping a charge with an arrow storm density and rate of fire are key. Composite and compound bows require a different, longer, draw to generate the same power so rate of fire is marginally reduced. They also both have less "snap" so per pound of draw so a released arrow goes slightly slower, shorter range, less stopping power.
Other issues; compounds and composites are easier to draw at a given draw weight for an untrained archer. Compound bows allow you to "hold the draw" while you aim making them more accurate at the cost of firing rate. Both of these make the weapons easier to use than a longbow but don't necessarily improve combat performance, you don't need "pip the ace" accuracy against massed targets for example.