Taylor,
I use the Boelube in all three forms, liquid, paste, and solid. As far as a difference, I think the Boelube does a slightly better job, but I have no way to quantify that. What I do like is that I can get the Boelube as a solid. I do a lot of large diameter (i.e. 2" to 4") hole sawing in sheet steel. spinning the hole saw against the Boelube stick is a lot easier than using conventional cutting lubes especially since most of the hole sawing is on vertical surfaces where the liquid lube runs off. The solid Boelube liquifies when you touch a warm or hot drill point to it, so it is easier to apply without a lot of excess running all over things. And, as I noted, I can use it to lube a tap that I am running through a stock to tap a lock bolt without worrying at all about getting cutting fluid on the wood.
Dave C