For precision shooting, the heavy varmint barrel is desirable. I had a Sako Finnfire II, which is very similar to the Quad -- except it has a walnut stock and the barrel is not interchangeable. It had the sporter profile barrel. The FFII is a great rifle, very well-built with excellent attention to fit and finish, and no doubt the Quad is equally fine. The problem for me was I found the rifle too light for serious bench shooting. When I was looking for a Sako, I couldn't find the Varmint variation.
I have tried the CZ route. I've had a number of different models, including 455's, 453's, and a 452 American, which I still have in a Boyds Pro Varmint stock. Aftermarket stocks can make a CZ more "shootable" on the bench, but often pillars and bedding are needed. In the end, unless you are prepared to add an aftermarket barrel for a 455, you are often limited in accuracy improvement potential. Changing a barrel on a 452 is not typically a do-it-yourself proposition.
The Anschutz 54 is more expensive than the Sako, but it has the advantage of being available in a number of different models, including sporters with heavy barrels such as the 1710 HB. Anschutz barrels are as good as they come on a factory rifle, and they have a well-deserved reputation for accuracy. The Anschutz factory stocks are very good in terms of bedding as they rarely need any work. Parts and service, should they be necessary, are very accessible with Anschutz. I am more than pleased with how my 54's shoot.
But for cost considerations, do not overlook the Anschutz 64. It is an excellent choice, a compromise among available precision shooters only to the venerable 54. Many shooters, myself included, can report that Anschutz 64 action models are a great way to get into precision shooting. The Anschutz MPR is a very good example of this and it is just a little more expensive than a Sako. Other Anschutz 64 action rifles with heavy barrels are available and they shoot very well, typically much better than CZ rifles.