If you live in Panama City, you'll probably choose an apartment. If you live in Boquete, you'll have mostly houses (some within gated communities) to choose from. When you get out in the beach community around Coronado, you might find yourself making the tough decision between buying/renting a house or a condo.
We've lived in a house now for less than a week, and it's been quite an education already. There's plenty to love, but there are a few things to consider.
A house is generally bigger than a condo, and there are still some great deals to be had when it comes to buying houses -- especially if you're willing to do a little work on the place. There is space for a dog or other animals (we have friends with chickens in their yard!), and usually there are already fruit trees growing on site -- or at least space to plant your own. The thought of picking my own mangos, grapefruit, and papaya is a very tempting reason to have a house and yard.
Of course, you then have to take care of that yard. It's been a long time since I've lived in a house, and I was shocked at how long it took me yesterday to water all the plants! Plus, we have the pool to take care of (though you can hire someone to do that for you twice a week for about $50 a month).
During the dry season, both houses and condos get dusty fast. In the house, there's a lot more floor to sweep and mop. Of course, you can also hire a maid for about $25-35 per cleaning, but we prefer to do things ourselves.
There are also more safety issues with a house. Panama in general is a very safe place to be, but like anywhere in the world you want to take precautions. We have bars on our windows -- most houses do -- and we take care to lock everything up. We also have a security system and we keep lights on in the yard all night.
Condos are naturally safer. Not only do you usually have security guards on site, there is usually only one entrance point into your unit (unless someone wants to scale the walls), and it's very difficult if not impossible to manage to get a peek inside to see if it's even worth breaking into. In addition, many condos have key cards or access codes to get through the lobby doors or up the elevator.
You also have a lot of amenities in condos, depending on the building: pools, gyms, spas, and more. Of course, you have a monthly fee associated with those things, but some of the buildings are quite affordable. If you're going to spend money on a gym membership each month, anyway, it's nice to have one right downstairs.
You do give up some privacy in a condo -- depending on the building, many balconies provide views into other units or balconies. You might have the share the pool with a lot of people. At the house, I've been running around the yard doing errands in my bathing suit all morning, and I don't worry about closing the blinds if I'm walking around clothes-free after a shower or something. We do have neighbors, but they're usually only around on the weekends, so I'll take a little more care then. With our own pool, we can enjoy a (plastic) glass of wine in there if we want to, without having the concierge tell us to take it back to the table.
It comes down to your personal preference and particular needs. If you plan on buying eventually, I would recommend spending some time in both a house and a condo before you make your decision.