OK, I'll give it a stab.
In my view, the final answer to your question is "false", but how you built the question was "true." :-)
The western church does take a more juridical approach to many things, while the eastern churches does take a more pastoral approach.
In general, the eastern churches just don't put the same level of emphasis on canon law as the western church. The eastern canon law isn't as developed as the western, and as a practical matter, you just don't hear about canon law much in the eastern churches. My personal opinion, which I think is shared by many eastern Catholics, is that an over emphasis on the details of canon law simply misses the point.
As regards annulment, I was curious and did some research. Anthony Dragani, an eastern Catholic expert who answers questions regularly on EWTN's Q/A, answered the question as follows: "the Eastern Catholic Churches do indeed have an annulment system. Historically this has not always been the case, but it is today." I would add that there is a formal process and a tribunal, at least in my church.
The Eastern Catholic Churches established annulment processes in the 20th century at Rome's insistence. The Romanian and Melkite Catholic Churches followed the Orthodox Church's practices as recently as 100 years ago.