Why not the axe?
The shield is Aquilonian, I dare to say. Aquilonians have the lion all over their equipments, Conan as a king had a full plate armor with a gold lion head on the chest plate. I may be wrong but Conan served as mercenary and soldier in the aquilonian army.
Believe me, I know my Conan history.
It's not that they have used the lion's head, as an idea that I like. But the lion's head itself just seems a touch overdone to me for a shield, too big, too raised, and too detailed.
The axe in contrast seems a bit basic and primitive, and so for me the two weapons don't quite balance with each other all that well, visually. Plus either that handle is way too short, or he's holding it way up the handle, neither of which looks quite right to me, at least at that angle anyhow.
If he had a more elaborate looking sword or axe that balanced with the lion's head shield better, or indeed a less elaborate, more basic looking shield that better matched the axe, I think it would visually work better for me, that's all.
Ultimately I'm nitpicking, and this is just my initial reaction based on a single photo taken from a single angle, so who knows how I'll feel when I can see and take in the whole thing. But right now I have a couple of minor nits to pick, that's all. And ultimately, it's all just a personal preference thing anyway.
Besides, I said it was a weird reaction...