You need another wrapper, something like this:
<div class="container">
<h2>Obvious Behavior</h2>
<div class="row">
<div class="col-lg-3 col-md-6 col-xs-12">
<div class="panel panel-default">
<div class="panel-heading">Title1</div>
<div class="panel-body">Content here1..</div>
</div>
</div>
<div class="col-lg-3 col-md-6 col-xs-12">
<div class="panel panel-default">
<div class="panel-heading">Title2</div>
<div class="panel-body">Content here2..</div>
</div>
</div>
<div class="col-lg-3 col-md-6 col-xs-12">
<div class="panel panel-default">
<div class="panel-heading">Title3</div>
<div class="panel-body">Content here3..</div>
</div>
</div>
<div class="col-lg-3 col-md-6 col-xs-12">
<div class="panel panel-default">
<div class="panel-heading">Title4</div>
<div class="panel-body">Content here4..</div>
</div>
</div>
</div>
</div>
<div class="container">
<h2>Desired Behavior</h2>
<div class="row">
<div class="col-lg-3 col-md-6 col-xs-12">
<div class="panel panel-primary">
<div class="panel-heading">Title1</div>
<div class="panel-body">Content here1..</div>
</div>
</div>
<div class="col-lg-3 col-md-6 col-xs-12">
<div class="panel panel-primary">
<div class="panel-heading">Title2</div>
<div class="panel-body">Content here2..<br>Content here2..<br>Content here2..</div>
</div>
</div>
<div class="col-lg-3 col-md-6 col-xs-12">
<div class="panel panel-primary">
<div class="panel-heading">Title3</div>
<div class="panel-body">Content here3..</div>
</div>
</div>
<div class="col-lg-3 col-md-6 col-xs-12">
<div class="panel panel-primary">
<div class="panel-heading">Title4</div>
<div class="panel-body">Content here4..</div>
</div>
</div>
</div>
</div>
<div class="container">
<h2>Bad Behavior</h2>
<div class="row">
<div class="col-lg-6 col-md-12">
<div class="col-lg-6 col-md-6 col-xs-12">
<div class="panel panel-success">
<div class="panel-heading">Title1</div>
<div class="panel-body">Content here1..<br>Content here1..<br>Content here1..</div>
</div>
</div>
<div class="col-lg-6 col-md-6 col-xs-12">
<div class="panel panel-success">
<div class="panel-heading">Title2</div>
<div class="panel-body">Content here2..</div>
</div>
</div>
</div>
<div class="col-lg-6 col-md-12">
<div class="col-lg-6 col-md-6 col-xs-12">
<div class="panel panel-success">
<div class="panel-heading">Title3</div>
<div class="panel-body">Content here3..</div>
</div>
</div>
<div class="col-lg-6 col-md-6 col-xs-12">
<div class="panel panel-success">
<div class="panel-heading">Title4</div>
<div class="panel-body">Content here4..</div>
</div>
</div>
</div>
</div>
</div>