Since the OP is asking specifically about portable units, it pretty much rules out the engine heat and diesel heaters that are built in. In a perfect world, I'd have both. Sometimes I'll fish in the cockpit or, if it's windy or raining, at the aft end of the saloon with the double aft doors open. A portable aimed at me is a great comfort. (OK, I've a complete softy after living in NorCal for over 30 years. Hard to believe I grew up with a newspaper route in Chicago!)
I have 2 Mr. Buddy heaters - Big Buddy
and
Portable Buddy.
I bought Big Buddy first for use on the boat because it holds 2 bottles for overnight heat without changing bottles, a quick connect plug in the back for their long line to connect to a 20 lb tank and it has an electric fan powered by D cells. I found that it's high heat setting (H-18,000 BTU, M-9000 BTU, L-4000 BTU) was too high for the boat's small spaces and the fan is needless due to the high heat output, even at low setting. Fans installed in the boat are much better at distributing the heat and holding condensation down. I also found the Big Buddy size to be a just bit too bulky for our vessel.
I was strolling through a nautical swap meet with Cpseudonym a couple years ago and found a Portable Buddy (PB) that looked like new that I bought for $5. It quickly replaced the Big Buddy (BB) and has performed much better. The 2 settings of the PB (M-9000 BTU, L-4000 BTU) are more than enough for us.
We usually run it on the low setting attached to a 20 lb tank. The threaded tank connection on the PB is really a non-issue for us. I carry 1 lb bottles for short-term use and have a refill adapter onboard to permit refills from the larger tanks. We don't do it often, but it's nice to have that capability, if needed away from shore.
Two features I consider critical for any heater with an open flame is tip over protection and low O2 sensor. Mr. Buddy heaters have both. I've never tripped the low O2 monitor, but the tip over seems like a good balance (NPI) of protection and usability. I've never operated the heater in rough boating conditions so I don't know if it would get finicky with pitching seas. Even the slightest bump of the unit causes the pilot light and the glow of the panel to extinguish.
IMO, the greatest hazard is combustible materials including fumes in the vicinity of the heater. You can't let your guard down with one of these things operating. That means no hanging galley towels, no drying wet hats or clothing, no flowing fabrics or scarves nearby. (Sorry Phil Fill, no dress up around these things!)
If you and your crew can keep a good head about running these things, they can be operated safely. Just don't do anything stupid...and if you do, tell us about it.
What happened to my BB, you may ask? It now serves as a garage heater in the winter for my retirement projects. I does a great job there when our temps dip into the high 30's!