they are often synonymous for "domestic" flights, but for international, there's a big difference in the soft product (you'll get better champagne, caviar on most airlines, more meal courses, and better ground service/lounge). The hard product varies from incrementally better to dramatically better (in terms of seat space, comfort and type), but in general, you can expect lie-flat beds in either class of service across the pond.

For your purposes, business class ought to be good enough.

What is a "reasonable" amount of money for you to spend to get there in business class? and how many miles do you have and in which programs?