It depends on what your goals and your criteria are for what you consider to be "better":
- Ease of Use
- Learning Curve
- Short Term Accuracy for a Beginner
- Long Term Accuracy for an Expert Archer
- Easy to Carry / Transport
- Faster draw and aiming cycle
- Faster arrows / more kinetic energy
- Easy to Repair
- Hunting or Fishing
And other criteria that I didn't manage to think of just now.
So for example compound bow are technically easier to use - after you figure out how to tune the sights. So there is a learning curve there, and it is a bit of a bell curve wherein the archer starts off clueless and has to learn how to adjust the sights in order to get the arrow on target - and once they learn that skill they basically plateau for a good while unless they also learn form aspects that improve their accuracy - which means they will still require hundreds of hours of shooting to get really good with it.
Takedown recurves are definitely easier to transport than a compound bow is. Transporting a non takedown recurve or a longbow is roughly about equally hard as transporting a compound, with pros and cons for both. Yes, the longbow is longer - but it is also lightweight and easier to carry. The compound bow meanwhile comes with a bulky case and is heavy. Like I said, pros and cons.
Recurve Bows are faster to draw, aim and shoot. It can be done so fast in a speed shooting competition they are the clear winner.
Compound bows you need to pull back, adjust the peep sight, line up the sight, check the level, relax, possibly go through several other steps such as controlling your breathing, and then shoot. Hopefully in less than 10 seconds, because after 10 seconds compound archers tend to start shaking.
Meanwhile the recurve archer has already shot 3 or more times in 10 seconds.
Compound bows do have an advantage in that they transfer more kinetic energy to the arrow, more efficiently. This results in the arrows flying at a faster feet-per-second (fps) speed, which does increase accuracy (depending on the archer's skill), and is handy for hunting.
Compound bows break easily. Surprisingly so in some cases and then require repairs from someone skilled at repairing compound bows. (Cough cough. Someone like me, who does compound bow repairs.)
In contrast if a recurve bow gets damaged it is easier to repair it, or replace the broken part. As someone who buys old compound bows just for their parts, I can tell you it is really difficult to find replacement parts for broken compound bows.
People have been hunting with bows (all types) for tens of thousands of years. Probably fishing with them for the same time too. (Perhaps they were originally for fishing, for all we know.) So when it comes to hunting and fishing, I don't think there is a clear "this one is better". Yes, the compound bow provides more kinetic energy and works well in the hands of a beginner, but recurves are faster on the draw and an experienced archer doesn't need sights to be super accurate.
Note - I do not agree with everything in the video below. 'Survival Lilly' is a decent shot, but you will notice in her archery videos that she makes a number of form mistakes that hurt her accuracy.