Which do you prefer?  

Both are nice...
but I'd choose the second one. The vines look messy to me, at the same time it softens the lines. So I guess depends on what you are looking for. But I love the horizontal fence.

No. 2
I saw a siimilar fence today and was admiring it !

Thanks for your replies....
Thanks for your replies.
I guess I should give some information.
While we like the slatted fence it's almost passe when it comes to modernist houses in Austin, TX. I love the clean lines, but my hood is full of them. Trying to get away from the homogenous Dwell modern look.
On the other hand, it's quite handsome and would be a design the next buyer might expect.
The hog wire / vine approach does a few things for us. We have really small lots, which not much room for privacy and not much opportunity for lush landscaping. Both of which we love.
We are not purist modernists. We like that it softens the hard lines and will be a place to add green life without the bulk of actual trees/plants that will crowd what little land we have. We would also be trickling in vines that bloom colorful flowers ... a little yellow here, orange there, pink etc.
We think this will give it a cottagy feel that we like.
But some poeple really hate hog wire.
Honestly, the wire/vine approach is more in line with the nice historical communities in the city. Usually found in front of redone craftsman, cottages, and the like.
We have done a few things to set our house apart from the norm in our modern community, but wouldnt mind more...
The slats do look cool though!!! You;d have to admit though, it is the typical modernist's choice. Perhaps becoming the 670 of the fence world.

Meet in the middle
I like the horizontal slats, but they could also look nice with just a bit of vines wandering up them. I think the second option would look great with or without the plants on them while I don't think the first will look as nice until you get a good amount of growth on it.
Our next door neighbor has a nice modern vertical slat fence, and in the summer it becomes a solid wall with all the ivy. In the winter the leaves drop off and the fence becomes more translucent, but still looks very nice. Of course, you don't have the winters we do, so yours will be more consistent in appearance.

Ok
it's far less ubiquitous over here!
Maybe you could use steel tension wires with vines for a more modern look ?

That is a good idea,...
That is a good idea, Pegboard thanks. I was thinking with heavy vines the wire would be more resistant to rot weathering do to the moisture of the plants themselves????
We would buy a fair amount of vines to ensure quick cover. What we don't spend on wood, I am sure we'll spend on plant life.

I'll send you some
kudzu, Whitespike. Your fence, yard, house and possibly child if you don't move him quickly enough, will be covered in a weekend.

Ha! Well, while I want it...
Ha! Well, while I want it covered quickly ... I am assuming Kudzu and anything with that kind of growth is more of a pest than anything!!
I will have to keep it cut around the gate... so I guess it can't grow toooooo fast.

Only kidding
about the kudzu, it grows like a weed here in the southern US and it is a pest!
Seriously, wisteria and smilax are two vines that grow quickly and would look good. What is hog-wire? Is it like chicken wire? Or is what I would call a chain-link fence?

No. 2
I'm in with the #2 vote. Looks great. Adds a sense of privacy without being defensive and alienating.
I feel that #1 would look best with no vines. Vines inappropriately done, can look messy...render 1 is that kind of look. Vines do not suit the architecture of your home. Your "wire" fencing would look best surrounded with bushes/shrubs flowers and rocks. More open and inviting without the loss of "containment"

How about
espaliered dwarf fruit trees? You can get the softness of plants, and geometry from Their shaping, and great food! They could be used in combo with either type of fence, or something even more minimal as mere supports. They are custom for a small space, and kids love picking fruit. Check google images for some great ideas. I typed "espalier fruit tree".

Kudzu
As a native Southerner, thinking of kudzu and red clay make me homesick. I know Kudzu is considered a pest, but I love how it transforms the landscape.
Riki is only partly kidding that your kid can't be stationary too long near Kudzu. If you stand in front of it, you can almost watch it grow.
"Kudzu was introduced from Japan into the United States in 1876 and is now common throughout most of the southeastern United States. Kudzu has been spreading at the rate of 150,000 acres (61,000 ha) annually."
Not that you'd ever want to plant it, but I think your climate may be too hot and arid for it to thrive.

Pegboard, you
must really be homesick if you are waxing nostalgic over kudzu! This time of year you should be thinking about butter beans, collards, buttermilk biscuits and deep-fried turkey.
P.S. Whitey, you still didn't answer my question r.e. hog-wire. Is it a chain-link fence or chicken-wire?

What a jungle Peg! I see...
What a jungle Peg!
I see a giant chicken, elephants, 30ft bikini clad woman or the rear view with small wings. pack of hound dogs, an out of proportion Gaetano Pesce UP5 chair (or Delorian car) and a long haired person kneeling down doing something. Bigfoot or de Frutti might be nestled in there somewhere.
Kudzu is an excellent example of why native species should be used in landscaping. The ecology in this photo is f^ed up! Will take decades to restore.