I have a Pet Gear play pen like the first one. It's great for traveling and I use it when visiting people. I'd only ever use it while she's in my sight (I would never leave her in it and go out somewhere), because 1). she can flip it on its side and use it like a hamster ball and 2). she is a hardcore chewer and could get through that mesh in seconds if she wanted.
The second playpen looks like a large dog crate without a top. With ZoE being the climber that she is (her nickname is "wee mountain goat") I wouldn't trust anything without a top. But it depends on your pup. I got ZoE at 6 weeks old (I know REALLY young) and she was fine in a playpen for the first month, by 11 weeks old, she was scaling walls and nothing without a top could confine her. I have a friend that has the same problem with her Chihuahuas, so she just uses a really large crate as a playpen. It works for her as she never moves it from the room it's in, but not great if you need portability.
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