Have both and prefer the paddles for a number of reasons:
The main reason is better grip, especially for bigger hands/fingers.
When the paddles on a spool/drum of a single action reel that is free wheeling ( knuckle dusting) when you are learning or not careful, happen to hit your fingers they tend to spin on the shaft more and glance off your fingers, transmitting less energy and therefore less damage to your fingers.
The issue becomes; is it better to have a smaller round handle profile that provides less grip, but is less likely to hit your fingers in the first place but when they do, do more damage to your fingers, or a larger wider flat handle that may be a little more likely to hit your fingers but do less damage when they hit and provide a much better finger grip.
None of the Islander moochers can do the kind of knuckle dusting damage that those larger diameter, heavy, hard handled old school Peetz reels can do. Further I would not even worry about it, as once you have any experience at all with single action reels, it is easily avoided. I have not had any damage to my fingers in decades with single action reels, with the exception of once playing a very large seal (250 lb or so) with great power and speed that had grabbed a salmon, and even then it was probably my fault.
The round handles I have seen on Islander mooching reels are smaller, hard and smooth which provides less finger grip and they can cause more hand/finger fatigue in a long fight with a very large salmon.
The wider paddles I am familiar with have all been of the softer rubber coated type with texture (like those on a newer Shimano 4000) which are less likely to slip out of your fingers when you want to reel in, especially if your hands are wet, cold and fatigued.
Paddles were not originally factory equipped on my Islander reels, so you may be paying to have them swapped out if you want them. Keep the smaller round hard ones as the next reel owner may prefer them.
This is one of those things where personal preference, hand size and what you have learned on and are use to is very relevant.
There may also be some resistance by some not to mess with a classic design and stay with the original ones for the same reason some don’t like to make “ugly” modifications to a classic car.