I will admit now, I am rather biased. Only ever used CBBE, and have never seen a reason to use anything else.
- Better over-all default shapes. Looks natural and in proportion.
- Photorealistic default textures. Textures also come with various sizes (from 4k/2k uncompressed to 2k/1k compressed, suitable for pretty much any computer or mod configuration.)
- Three default shapes, each coming in nude or a choice of two kinds of underwear styles.
- NMM/MO support.
- BodySlide was made for it in mind. With BodySlide, the shape can be however you want. Also includes TBBP/HDT support.
- TexBlendLite to fix neckseams with almost any face retexture mod and the default body textures.
- Huge (500+) mod list on the page with links to the mods and a little key saying what the mod contains. A CBBE/BodySlide conversion of Immersive Armours is also on the list.
- Still supported by Caliente and Ousnius, and gets periodic updates when necessary.
- Still the most used and endorsed body mod.
- Needs more polys to smooth things out. Some parts of it look a little jaggy due to this.
- Leg shape could be improved.
- Original shape was bad, and this seems to have clouded peoples' minds towards it, even though it's gone through a lot of changes over the years. Many people still seem to think it's the same jumbo-breasted thing it was in 2011. Every time someone posts a thread like this, people seem to always talk about how 'CBBE is just huge boobs', even though the UNP breasts have been larger than CBBE Curvy ones for years.
- Original name was bad. Ditto above about people thinking negatively of the mod just because of its early days.
- More polys.
- Better leg shape.
- Lately seems to have more support than CBBE, most likely due to the above mentioned cons.
Not going to do cons, as over the years I've found many UNP-fans tend to be rather...aggressive about other peoples views on it. Which is a con in itself. =/
TLDR: I prefer CBBE. Use what you want.