Keeping in mind that I don't own and have never used any kind of fursuit myself, this is what I've gathered based on things I've read.
Partials
Pros:
- Cheaper
- Not as warm to wear
Cons:
- Sometimes restricted by how much the partial covers (e.g. if you buy short paw sleeves/gloves, you're restricted to wearing long sleeve shirts if you don't want to show any skin)
Depends on personal preference:
- Tends to look more naturally human
- Some people may feel it doesn't entirely "complete" their fursona or character
Fullsuits
Pros:
- Don't have to worry as much about what clothes you wear with it
- If you're looking for a feral (quadruped) suit, this is the way to go
Cons:
- More expensive
- Builds up a lot of heat inside the suit
- Depending on how the suit is made, it can restrict movement a bit
- More fur to keep clean and tidy
Depends on personal preference:
- As it tends to be baggier and add more bulk to your body, the overall look tends to be more stylized or toony
- Gives the appearance of a more "complete" character
In the end, it really comes down to which one personally appeals to you more and what you can afford.