What follows is written in a friendly tone of voice and only to help you consider something. I don't claim to be an expert on this topic, so take my comments with a splash of saltwater. However, I have spent a lot of time considering which type (mono or multi) to get and why and this has influenced my comments below.
I think the
budget and your boat choice (which particular boat and size and condition) are most important for a good decussion on this topic.
Why?
Because if your
budget is low, you will be choosing between old
boats and on the catamaran side it may not be possible to find a suitable cruising boat. For example, if one is limited to just $75K, I think one could find a clean, nice condition older
monohull, that could take one around the world. But, that same budget would restrict one to an older, smaller, catamaran, if one could find one in the
price point.
If you have a large enough budget (and I suggest
posting the maximum "asking price" you would consider) then it helps define the available options.
IF you have $250K or more, then I think a catamaran (e.g.
Lagoon 380) would probably be more comfortable for most people in most locations for most typical coastal cruising.
But, with that same $250K I could pick a real strong, big, "blue
water boat" that I would feel comfortable taking to extreme locations, and around the world, and it would be a monohull.
So, I think to help you, it is best to define what is possible (the asking
price limit) and where you want to sail, and if you plan on
living aboard it permanently, and if you intend to have more than just yourself on the boat, etc. Those things matter, as I see it.
Good luck on your choice.