Just FYI: My 375 H&H is a BRNO 602, not the newer 550 action. The 602 is a better buy if you can still find one. The 550s I've seen & handle at the shows looked & felt rougher, in my opinion.
I shot mine a while and then had it customized by Lon Paul, a riflesmith specializing in these types of rifles. For a very reasonable cost he can really turn one into a fine Big Game rifle. His metal & stock work are excellent, especially the way he eliminated the "hog-back" feel of the European factory stock. Recoil impulse feels much different. The .375 H&H web page has pictures and information if you're interested in what the improved "conversion" looks like.
These guns in general are decent shooters out of the box but can really be made to shine thru having some basic things done like bedding and trigger work. My 375 is MOA with some factory loads and several handloads, and frequently sub-MOA if I do my part. People at the range often mistake it for a much more expensive gun than it actually is, even with the custom work.
On the subject of CZ-type rifles, someone mentioned the no-longer-imported "mini-mark X," in .223. Not many made it into the country, or so I'm told, but they were imported in .223 & 7.62 Soviet. I have a .223 - it's really a carbine, sporting a slender, nicely grained stock and a 20 in. barrel. I love it. All I added was what I call the "basic 3" by a local 'smith: (1) trigger job (smooth as glass), (2) proper bedding of the action, and (3) channelling of the barrel. My 'smith did great work and it shoots better than some of the heavier, longer barrelled American stuff I see guys drag out at the range. It too is a sub-MOA shooter with certain factory loads and handloads. (The fun is in playing around with the different bullet weights and loads available for the .223). For some reason it really likes Cor-Bon's .223 55g HP (moving at a box-flap velocity of 3200 fps), so that's a sub-MOA factory load I shoot often. Here in the midwest, it's a great little 'chuck gun, or any other varmit of opportunity.
In my opinion these rifles represent one of the best buys on the market.