Watercooled engines are more efficient. You can run them at higher compression ratios for a given octane level, the parts can fit together more tightly (effects oil consumption), etc. Also, the watercooling keeps them at a more consistent temperature regardless of the season. My Bug was kind of finicky in extreme cold weather (below 25deg) and I tried to take it easy on extremely hot days (above 95deg).
Aircooled engines are pretty simple, but you have to pay more attention to oil temp/pressure, ambient air temp, keep the engine clean (affects cooling), etc. I never had a problem with my Bug overheating, but I was anal about keeping the oil topped off (never let it get more than 1/2qt low), the engine clean, and I had a mechanical oil pressure gauge so I could monitor the lubrication system. I would go on Bug-Runs in the mountains, during the summertime, and not have overheating problems that my fellow drivers would experience.
Chris