Grovey - as to why H4895 over Varget: I have used both for many years in .223 Rem F-TR loads with 88-95 gr bullets. In my hands, Varget has never come close to the precision I can get with H4895. Others may have had a different experience, but I have observed the same trend over a number of years. Second, with a slightly lighter bullet (i.e. 77 gr), powders in the burn rate range of H4895 to slightly faster should be well-suited to the task. It's important to point out that I am in no way bashing Varget. In my .308 loads, I don't use anything but Varget. Nonetheless, Varget would absolutely work in the OPs specific situation, so we're really slitting hairs when we talk about "slightly" faster powders than Varget being optimal.
Also in my hands, H4895 typically tunes in at around 25 fps or so faster with heavy bullets than a comparable Varget load in .223 Rem. Likewise, IMR4895 tunes in at around 20-25 fps faster than H4895 in comparable loads. Does 25 fps really make a difference? I would argue that for most shooters, a 25 fps difference would be way down in the noise. Unless you're really pushing the upper end of the envelope, ~25 fps just isn't enough difference in velocity to make a strong argument either way. However, the velocity difference may be larger with the OP's 16" barrel. Regardless, unless the OP is planning on trying to hit the highest node possible at safe operating pressure, the minor difference in velocity won't mean much.
Finally, kernels of H4895 are noticeably finer than kernels of Varget. Obtaining optimally low ES/SD values is sufficiently difficult in the .223 Rem case, largely due to its small capacity, that some may find the slightly smaller kernels of H4895 a little easier to precisely meter than Varget. Again, none of these issues/differences between Varget and H4895 should be a deal-breaker. Either one will work just fine. But if I was in the OPs position and had both powders on hand, I would reach for the H4895 first. If all I had was Varget, I would use it without a second thought.