I'm not home at the moment, so I don't have my OCE D&D Boxed set to refer to. Swords & Wizardry White Box doesn't have a thief class, but Swords & Wizardry Core does.
Here's my comment / observation:
S&W Core's Thief skills are percentile based (except for Hear Noise) and increase with level.
In Delving Deeper, all of the Thief Skills are D6 based: 3 or higher on a D6 indicates success. Level doesn't not increase this.
So, Delving Deeper has a bit of LotFP Weird Fantasy thief to it, but not quite.
I'm fairly sure S&W Core is closer to the original thief class.
I'm not sure if I like the DD version of the thief, but it does make him more relevant at lower levels.