From your picture, it looks like you're running a Soft Top and half doors now.
Switching over is easy - just find a hard top to buy. You'll need to remove some hardware from the soft top, like the drill-in header bar above your windshield. You'll need some gasket tape for the hardtop. Very minor things, and it's easy to install a hardtop.
Here are the bad things:
Hardtops ain't cheap. They're hard to ship, so make sure you include shipping costs when you price them out. They're hard to store over the summer, especially if you don't have a garage.
And on a YJ, you need to be careful about matching your doors. There was a "miscommunication" back in the day between the soft top groups and the hard top groups at Jeep - soft tops used a square upper door, and hardtops used a rounded upper door. So your upper doors might not work with a hardtop that you buy.
As far as which is "better" - I can't answer that. It's a personal thing. And personally, I like having all the options. So I've got a hard top and a soft top, and a Bikini top. But that's not reasonable for everyone.
myself, i like having a soft top. i can take the top down whenever i want and i can take it off and put it up all by myself. i also don't have to worry about where to store it once it is off. however, a hard top make the jeep more secure and deters thieves. i sold the hard top on my cj and went with a soft top b/c i like the open air feeling.
(BTW, howdy neighbor. i'm across the bridge in holland/milford)
My "new" Jeep is a summer beater. When my past jeeps were my only vehicle, I'd love to have a hard top. Now, I'm looking to trade for a soft top. I'll never drive it in the winter, never need to secure it, etc...
Depends on your use...if it's your "only" car, then a hard top is the way to go. If it's a toy, soft top is easier.
The best reason for a hardtop is for security as jgano mentioned. As for the winter, its not that much warmer than a softtop since they're both not insulated but glass windows are nice when everything ices up.
"Roads? Where we're going we don't need roads!"
'96 XJ 4.0L, AW4, lots of miles, project Jeep.
'08 JK 3.8L, NSG370, ragtop, daily driver.