The BEW is an alright engine, the first of the PD engine type(higher injection pressures with more precise timing allowing for better power and lower emissions compared to the ALH). It had cam issues, as does the BRM(found in the 2005.5-2007 Jetta TDI). It's not a "common" problem, it's an inevitable problem. The BRM certainly had it worse off for cam issues than the BEW. So you will run into cam issues with either engine, but if the car had correct oil it's whole life, it will take hundreds of thousands of miles to wear out, but most don't use VW spec oil, so it accelerates wear.
ALH is a clear winner in terms of fuel economy, mod-ability, reliability, and longevity. For power, the ALH was rated for 90hp/155 ft/lbs of torque. BEW at 100hp/177ft/lbs of torque. It's not a huge difference, albeit, slightly noticeable. Another thing to consider, is that the BEW can have injector problems. VW quoted my neighbour $1,000 CAD per injector for his BEW! He found a junker TDI and replaced all 4 for $200. They only had 80k miles on them and 30k down the road with these "new" injectors, they've gone bad again. I've heard similar stories.
To say the ALH is bulletproof, is an understatement. If you know diesel trucks, it's like the 7.3 of powerstrokes. Undoubtedly the most popular and the best diesel put into their cars. The ones that followed certainly declined in reliability and economy.
I'd say, find an ALH and mod it. They are an amazing engine, and they are generally known as the diesel engine that made diesels attractive again in passenger cars.