While most here are probably much more dedicated varmint hunters than I am these days, here are some thoughts.
Both calibes are so dang cool & both have changed the varmint world forever! Love...love the .204 R for so many things; I will always keep one. But...there is something so cool about all these .17's. I.E. 17 HM2, 17 HMR, 17 H-Hornet, 17 Fireball & of course the 17 Remington...you need one of each. The latter is definitely awesome as well as proven winner for your application. If you don't need the distance or the extra foot pounds (.204 R) it will do just fine.
Regarding CZ's, I fell in love with Czech firearms nearly 3 decades ago before they were so well known. (I.E. Brno's/ CZ's) These days, as always, I think the CZ 527's are pretty tough to beat for the money.
To that point, I actually have at least one in every caliber available as well as a few customs & Wildcats in calibers not currently offered. I even have a 527 in 6.5G on order...hoping to see it before spring. So I guess I'm committed...or need to be.
On the topic of CZ Varmint or American (standard) barrels it really comes down to YOUR use & applications. While they are available in both profiles for .204R...they are only available in Varmint for the .17 Rem. (I too think CZ is missing the boat on that.) To me they are definitely lighter & more balanced for my style of shooting & hunting which is rarely at a bench. NOT that there is a thing wrong with that...I just prefer walk-about & want to keep them lighter for my application. (Accuracy is the same for both.) Yes the Varmints stay cooler longer & hence retain accuracy longer before they are heated up. But...they take that much longer to cool off. For my needs with a either a .204 R or .17 Rem I rarely need more than 3-5 rapid shots. If I do, I either will switch rifles or use something else. I.E. 17 RF's or a 17 H-Hornet.
I USED to have several Varmints...both lengths/weights. They are all gone now & every single one of mine is a American standard profile barrel including my .204 R. Even my 527 in .17 Rem is an American...one of the few out there. I.E. custom PacNor barrel. BTW, you could easily rechamber one of their 17 H-Hornets in an American if you really wanted that profile fairly inexpensively.
Not to get too far off topic but right now my favorite is in 17 H-Hornet...tough to beat the efficiency of 3650 ft/s & being able to load nearly 600-700 rnds with a # of powder. But for your needs as stated it is tough to go wrong with either the .204 R or .17 Rem. Some say that the 20's are a tad quieter & of course the .17 Rem has the characteristic & piercing "17-Snap". The .204 R definitely reaches out & keeps terminal velocities further out...but tends to destroy things more...which can be good or bad depending on your perspective. But the .17 Rem is so great at what it's good at. As I said, there is something so cool about 17's. Sorry so long winded...fun stuff!
Best of luck...keep us posted!
Cheers,
TOU