I have had both, but both were early pre-ban guns. Both were good guns. I do not know about the new Bushys. You could always buy the parts you want and I bet some OSAers would help you build a great gun at a good price.
My, noob advice......PM Pinkhammer for a complete lower, order a complete upper from JSE. May take a while for the upper but in the end you have a good gun for a reasonable amount of cash.
If it was the 2 of them, I would pick the Bushmaster. I heard a few years back that Olympic Arms used a cast lower and did not hope up as well. I am not 100% sure of this.
Why just those two? Neither is very close to the top of my "buy" list, but of them, I would go with Bushmaster, because they at least offer chrome lined barrels.
I think there are many other quality AR out there. It gets to a point that you're paying for a name. Daniel Defense is good for the money. I would pick Bushmaster over the other brand. I like building them from all the different quality parts on the market. I've been trying to get some parts from Armalite for about 9 months now. I can't recommend them.
I know it will sound funny, but with all the crap going on whatever is affordable. Bushmaster makes a good one, Stag ( I have one) and also DPMS is a great one for the money. Smith&wesson m&p15 are also good.
Used might be the way to go but there are some people who have pretty high prices. Seems you can get lucky and find a nice used one periodically for under 1k. 1000rnds of ammo and 10 mags min is a pretty good start.