The spinning set up will cast a 1/4 oz further in my opinion since I have tried this before with a set of spinning and casting with the same brand reels and same length poles I can cast normally with 10# mono the 1/4oz bait 10-15 yards further.
The question is too vague to give a simple answer. Casting distance is is a function of technique, rod length, rod action, lure weight/type, friction, and ?? probably more.
Let's say you have a Shimano Stradic 2000 series spinning reel. 10 lb mono or FC is a bit heavy for that reel. The line wont flow off the spool freely and may even birdnest on you. A curado will have no problems with 10 lb FC....
Let's say you have the proper size reel for the line type/size you're throwing but you only have it spooled up 1/2 full. You'll lose a bunch of casting distance because of the additional friction between the line and the rim of the spool.
Let's say you have two 7' rods, but they are of a different action. The one that loads up "properly" is the one that will casts farther, all else equal.
Line....OK, so you use a wiry FC line on each reel type...the baitcaster will be affected less by wiry line than a spinning reel.
How well is your baitcaster set up and how good are you at casting? If you switch off all the clutch weights and loosen the spool tension, you can throw a lot farther....but you'll backlash like crazy if there's any breeze or if your rod is too light on action....
Depends on the reel, line, and skills of the user. Personally I can cast a 1/4 oz (small) popper further with more accuracy on a spinning rod, but I have to some add caveats.
I have spent 30+ years using spinning rods, and have only been using baitcasting tackle regularly since about 2003. (Some might say I am not very good with baitcasting tacklem but that is not true. I have very good accuracy and distance pitching, side arming, and overhand casting. Its just that I have expert skills with spinning tackle learned from a very young age.)
I use a larger than normal (than most people would select) spinning reel, even for light line. If just takes to much line I'll use a backing.
The spinning reel needs to be full, but not over filled. The difference in casting performance of a spinning reel drops dramatically as line level drops.
I also use one for casting into heavier wind with jerkbaits and medium to small cranks when that is the pattern. I can fire a low trajectory two handed snap cast with a spinning rod that would be all but impossible for me to do with a bait casting reel.
My favorite popper rod is a Quantum Tour 7' medium (no longer made, but I bought spares) with a Daiwa SS Whisker 1600. The reel takes some getting used to as it has a positive kick over stop. I imagine any similar size reel of good quality would do the job. I've got a Shimano spinning reel on my backup rod and for guests. Both are spooled with 10lb mono. I like Suffix Seige, but I think one has Izorline on it, and works well. I like the 10lb mono because mostly I throw poppers on these rods (except in the winter) and it floats better than flouro carbon.
Can you cast it directly into winds gusting 20-35 mph? I can with my spinning rod. Not that I would be casting a popper in that kind of wind. LOL. Crankbait, jerkbait or spinnerbait however... That can sometimes be a pattern. I'm gonna have to go toss a rico on the scale I thought the regular rico was slightly heavier than that.