Well, I have done both. I have built myself a 416 Rigby on a CZ 550 action, have bought a VC double in 500 Nitro and modified a Win Model 70 in 375 H&H by changing out stocks and re-chambering to 375 Weatherby.
I also bought and ordered a CZ 550 in 505 Gibbs from the custom shop, but really that was too nice to hunt with. Since sold.
Of all, the 375 sees the most action, the 416 is next and the 500 is a serious backup rifle which I have used in anger twice...yep both barrels on ONE hunt here in Australia on Water Buff.
The 375 Weatherby is a serious step-up from the H&H, it is a genuine 200fps+ gain with all bullet weights and hammers Buffalo with authority. It is visibly noticeable on how much harder it hits. Both it and the 416 have similar reactions, nose down on impact and most bulls never recover from the first hit. I use Woodleigh bullets in both rifles, a 300gr PP in the 375, due to it's higher velocity (2830fps), and 410gr RNSP in the 416 (2520fps).
Oh, and Wayne at AHR no longer offers his CZ modifications, with CZ dropping production, there had to be a compromise on his business. His custom work took over on that.
Cheers.