IMO either, though the split rail fence would need a wire fence or support to give it something to climb. Clematis climb by twining leaf petioles around a support, so it has a tough time grabbing anything larger than about pencil diameter. Can you widen the bed a bit by the utility box and move the grasses out, dividing the as you do and then plant the clematis such that it will grow over the top of the utility box? It’s large enough to hide the utility box with a bit of guidance.

Personally, I'd pick the fence. An established SAC is a big vine....very BIG!! It will outgrow a 5' trellis in a matter of weeks! And then want to take over the rest of that bed and smother the utility box....which might be OK if you never need to access :-)

And I have also found that wire or additional guidance is typically not needed to grow on a fence. As long as you can train it to grow up onto the fence (something like a couple of bamboo poles tilted against the fence), then once there, it will make its way happily along the top.

Being very invasive ( here in Ok.) SAC is beautiful. I live in NEOK and I have it growing on the side of my shed on a trellis. I cut it down immediately after it gets done blooming so the seeds don't fall! It's been there 5 yr. and hasn't spread but it does cover the whole side of the shed.

Enjoy yours.