Is there a better saw to use than a chain saw?
Yes most definitely. A chainsaw will do the cutting for sure, but the resulting cut surface will be a bit, ah, rustic. Chainsaws have never been accused of producing particularly smooth/clean cuts :-)
Very related previous Q&A: Crosscutting 18" diameter logs by hand.
This doesn't mean you can't do the cutting using a chainsaw, it'll do the job very efficiently. But you do then need to smooth off the cut surface quite a bit to make it flat and smooth.
You didn't ask about this but further processes are nearly always used to finish off rounds like this.
Probably your best bet to flatten and smooth if you can get the chainsaw cut fairly even is with power sanding, maybe with a belt sander to begin with using a coarse grit, then switch to a finer belt. So you might start with 60 grit (possibly a little coarser) then move to 80 or 100.
Then you'd switch to a random-orbit sander to smooth off, e.g. using 100 then 150 then 220 paper, possibly finer depending on the surface quality you're going for*.
Prepare yourself though, even with power sanders this can be quite a bit of work even with softer species — you're working an end-grain surface and end grain is the toughest part of the wood. If you're using a harder species, particularly a hard hardwood, this can be extremely tough going so you need patience and perseverance.
If you have a router flattening rough-sawn rounds is one of the things they can do brilliantly, using a simple homemade jig:
This way you really don't have to worry that much about how rough the chainsaw cut is since the router can easily tackle an unevenness of 1/2" (13mm) or more, as appears was the case in the photo above. Note: you wouldn't take that much off in in one pass, you'd use numerous shallow passes so as not to over-stress the bit, the bearings or the motor.
More on this sort of levelling jig in this previous Answer: Flattening the face of a board without using a jointer.
*This relates to how you want to finish. Finish type (if any) is a factor in how finely you want to sand any surface. If you'll be putting on a full film finish (varnish, lacquer, epoxy) you can get away with some fine scratching because the finish fills these up. If you intend to leave the platters bare, or just give them a light oiling then generally you want to finish to a very high level (240 grit or higher) because surface defects are very easy to see.