Here are the major drawbacks:
1. It is an EXPENSIVE setup. The oven alone is going to set you back a few thousand. Not to mention the special connections you will need to make your propane system "boat safe" - which brings me to point number 2:
2. Propose is heavier than air = BOOM! If you are going to go with propane, don't skimp. Take the proper precautions. If you have a leak, the propane will accumulate in the bilge of the boat, building higher and higher until one day you unsuspectingly light a watermelon scented candle and KABOOM!
All I am trying to say is that if you go with propane, spend the cash to do it right.
Our boat didn't come with propane installed, and we didn't have the cash to set it up, so we used a non-pressurized alcohol stove-top made by Cookmate.
The two biggest benefits to these guys are that they don't blow up, and they are cheap! They typically cost about $250.00 - which is pretty cheap compared to the $1,000+ you will spend on a propane range, not including the hose and connections.
The cookmate uses re-fillable wicks. You simply pour in more alcohol when the wicks stop burning.
Alcohol can be purchased at hardware stores or painting supply stores. Don't believe me? Read the back of the can! You will see a section titled "cooking fuel".
A lot of sailing books recommend buying high grade cooking alcohol because it burns "clean". We never had a problem with standard hardware store alcohol. I recommend you experiment and do whatever works best for you. If your pots and pans are all turning black, you have probably gotten a hold of some crappy alcohol.
If you are going for a long cruise... make sure you buy just one can to test out house it burns before you stock up with a 5 gallon jug.
The alcohol you pour into the wick will evaporate, so it is worth your while to buy these little rubber seals for the stove. These seals might come standard on a new stove. Our stove came with the boat... and it was missing it's seals, so we bought new ones.
The major draw back to an alcohol stove is that they don't burn very hot, so it takes a little longer to boil water for Ramen noodles :) Another item that was missing from our inherited stove were these little flame diffusers.
Clearly labeled "do not remove" - the flame diffusers from our stove were missing! These probably come standard on a new stove. We ordered a pair while we were holed up during bad weather in Annapolis. I was so excited to be able to cook more than one pancake at a time!