Riverby is right; context is the deciding factor here. This question can't really be answered without context. However, I'll muster up a little impromptu context here:
For example, one would "pull on a condom." (Though, 'put' is the preferred verb here). Yet one would "pull a condom over their you-know-what." ('Put' still being preferred).
For a more "appropriate" example:
"I'm going to pull the sleeve onto the shaft."
^Simply states that you're putting a 'sleeve' on the 'shaft' (and subsequently leave it there or it subsequently rests there).
"I'm going to pull the sleeve over the shaft."
^Emphasizes the covering of the shaft; in many circumstances implies that the 'shaft' is more or completely covered by the 'sleeve.'
In addition, using 'on' (as was posted) instead of 'onto' could change-up the sentence a bit.
"I've found the shaft and I'm going to pull on the sleeve."
To take this in one more direction:
"They pull the sweater over their head." or "They pull the sweater on." You would not say, "They pull the sweater over." because in this case the word 'over' signifies that there is something specific that needs to be pulled past/over/around etc.
In the case of the 'shaft,' one could be pulling the sleeve overthe top of the shaft. In turn, one could pull the sleeve on(to) the shaft, and nothing specific about the shaft (its head/top/bottom etc.) is mentioned.
I posted this just to entertain your (the original poster's) thoughts, so you may realize what sounds best to you and how you will use it.
Ultimately context is key, and they're relatively similar expressions.
Hope this was of some help.