Long post incoming:
Our .22 rifles are our staple shooters for nearly every range trip. Before retiring I shot .22 BR with my club, but our new location doesn't have a BR match. We do have a 'Pig' match, where we shoot reduced size steel pigs at 200m, and my wife and I both shoot that match. It's very challenging!
I shoot a Tikka T1X and my wife shoots a CZ 457 Varmint Pro. Both are in KRG Bravo stocks, and the CZ has a Timney trigger. I recently bought a CZ 457 in .17HMR to shoot the pigs when the wind is blowing.
Tikka
T1X @ 50yds with CCI SV
T1X @ 50yds with SK STD
The T1X was my first 'precision' .22 rifle. I was really just looking for a suppressor host, but nothing was available at the time, and the LGS had a T1X on the rack, so I bought it. I was immediately impressed with the accuracy.
It's very good with CCI SV, and Norma Match 22. Groups are about the same, but IME the Norma has slightly less flyers and performs a little better at 200m where we shoot our pigs. The pic above is a practice target with the size pigs we shoot at 200m.
The factory stock was terrible, so I replaced it with a KRG Bravo. IMHO a good stock that you can dial in to fit you is critical to consistent performance with a rifle. The Bravo has a lot of great features at the price, and has worked very well for me. My Tikka still has the stock trigger, and it's still my preferred .22. It gets shot 100% suppressed with a Mask HD.
CZ 457 -
CZ 457 @ 50yd with CCI SV
The CZ is a solid performer. Ours likes CCI SV, which makes me happy because it works well in all my .22s so I have a lot of it. I replaced the original AT-One stock with the KRG Bravo to dial in the fit. I also added a Timney trigger. Interestingly, the CZ doesn't like my Mask HD suppressors, so we shoot it unsuppressed. One of these days, I'll get around to doing some more testing to try to figure that out.
The CZ does have the advantage of a better aftermarket than the Tikka, and barrels are easy to swap, which could be important if you're looking for that last 1-2%.
The CZ is primarily my wife's rifle at this point, and I haven't shot it months...
Ammo -
Ammo is the key to accurate .22 shooting. I have found CCI SV to be very good for the price point, but you will deal with 2-3 flyers every 15-20 rounds. Norma Tac-22 and Match 22 are about equivalent for accuracy, with the Match 22 having a slight edge with a smaller number of flyers. The Norma bullet has a better BC and performs marginally better at 200m for us.
You can really go off the deep end with match .22 ammo and spend up to $25-30 a box for the top level ammo. I did a bunch of testing when I was shooting 50m bench rest and decided the additional performance just wasn't worth the $$ for me for a 'fun' competition at 50m. I'm now looking into doing some more testing, because at 200m the difference is more significant. Of course, at the moment, there's not much ammo available! I can't even re-stock on Norma Match right now.
Bergara -
I don't own a Bergara .22. Amongst the shooters at our local range there are only 2-3 I know of and reports are mixed. The biggest 'advantage' of the Bergara is R700 compatibility, though the aftermarket for the CZ and Tikka have both grown quite a bit in the last few years.
I do have two centerfire Bergaras: a Premium in 6.5CM and a B-14 Ridge .223 I built for my wife. Both in KRG stocks with Triggertech triggers. The 6.5CM is a laser. The .223 is brand new, and I'm still testing ammo. The .223 replaced a post-bankruptcy Rem 700SPS that was not impressive. The Bergara is a much nicer rifle out of the box, and already shoots better, even though I'm less than 100 rounds in.
Bergara Premium 6.5CM
Bergara B14 .223
TL, DR -
I don't think you'd be at all disappointed in the CZ 457, but if I were to buy another rifle tomorrow, it would be another T1X. For me the only compelling reason to buy the Bergara is to get the R700 pattern compatibility.