IMHO Fushigi Yuugi is one of your archtype anime. 
Its great stuff and lots of funny & dramatic 
moments. There are also lots of sappy moments 
filled with teenage girly angst. (Not that this 
is a bad thing - But you have to like or put up 
with that kind stuff).

Tenchi is your archtype boy comedy (like AMG and 
others) it features light comedy and also has a 
few dramatic moments to keep the story moving. 
There also a bunch of "boy" type moments (again 
not a bad thing but many female friends watching 
it have labelled it "typical!").

On balance although I love both - I'd go for 
Fushigi (despite all its shortcomings) as it 
really does tell a dramatic story (IMHO it takes 
too long but it does tell one). Tenchi just like 
that - a bit of fun.