Interesting, never thought about going smaller.
Are full chisel chains the ones with the big warnings about kickback? Should I be concerned about that?
What's the gain in going to 3/8"?
3/8 pitch (regular 3/8 that is, not 3/8 low profile) makes a wider kerf. For saws with more displacement, it's a better choice; it's easier to sharpen and it stays sharp a little longer (assuming other factors, namely cutter shape and hardness are the same). Since it takes a wider kerf, though it takes more power for each cut. It can be run on 50cc saws, but generally most people don't run 3/8" until you get to 60ccs.
.325 has benefits too, namely on small saws each cut will be a little faster because it's less work to make a smaller kerf. It may also be a little smoother in the cut and less grabby when limbing because it has more cutters. There are other variables at play, though.
You should be concerned about kickback, yes. Chainsaws are dangerous, but you probably already know that. All chains have a potential to kick back. Reduced kickback chains have a different depth gauge design. Depth gauges aka rakers determine how much bite the cutter takes with each pass. On reduced kickback chains, there I'd usually a second part alongside the depth gauge that prevents the cutter from cutting while it goes around the tip of the bar. For me, there might be a slight speed advantage to regular aka professional chain, but the main advantage is when sharpening. When you have to take the depth gauges down, which I do about every three filings, it's much easier on regular chain because there's simply less material to mess with.
Regarding full chisel vs semi chisel, full chisel cuts faster and is maybe a little smoother in the cut. Semi chisel holds up a little better in dirtier wood. Semi chisel is also easier to file by hand. For the majority of my cutting needs I prefer semi chisel, non-safety chain. As you can see, though, there's lots of options.