Chris
Copyright (broad stroke) is the ownership in the material which includes the right to reproduce and otherwise exploit the material.
If you sell the copyright (subject to various legal nuances depending on where you live) the rights transfer to the new copyright owner and you no longer have the rights to do things with the material.
An unlimited use license would effectively do the same thing with the caveat, depending on the agreement, as to what you can do with the material.
For the most part it will come down to drafting and what you want to accomplish. For example, let's say someone wants to use an image in a book, you can license the image just for that book or including ancillary uses such as posters advertising the books or limited runs of the books. Unlimited means they can do what they want, put it on t-shirts, bumper stickers, the rest. In an umlimited license photo credits may be easier to make sure are done, as oppossed to an out and out buyout where they just may want to walk away "clean" with no further contractual obligations.
I am not sure how large the entity is or what type of material you have shot, but whether you want to transfer the copyright comes down to what makes you happy and if it makes financial sense.
If you have the only shot in the world of a Great White Shark dancing in a top hat and cane chances are there can be more sources of revenue down the road and a buy out should reflect that. On the other hand if you have a really great shot of a French Angel and you are offered a good chunk of change, you will probably get good shots down the road.
As to the difference in the pricing between a transfer or an unlimited license, for the most part think of them as practically the same thing, If there is a market for the photo and someone else can do exactly the same thing as you, you will be competing with yourself all the time. Not to say that you may not beat the big company to the punch.
As to actually transferring copyirght, yeah it can be emotional. The things we capture become an extension of ourselves sometimes.
As an aside, it may be something where you give them a limited license to do what they want - you get the credit, they can do what they need and you can keep the relationship going.