In general,
Round reels: more line capacity, better casting distance IMO, and little better drag
low-pro reels: easier to palm, lighter and less bulky
It really depends on what baits you are throwing and what rod you are using.
I use low-pro reels for lighter swimbaits (ie: 6" hudds) or baits that I need to work. (ie: topwater, wakebaits, walking baits). I pair those reels with rods up to 7'6". I usually use braid or 20lb mono or less for this setup.
I like using round reels for heavier swimbaits ie: 8" hudds. I need more line capacity because I'm using 20-25lb mono. And I pair this up with longer rods 7'9" and over. These rods usually have a longer butt section so you can tuck the butt section under your arm and the round reel will feel comfortable. I don't need to palm round reels fishing this way.