using limit instead of seeking

Would there be any reasonable performance gain in using LIMIT in an sql
query to print pages of results, instead of seeking to the desired record
and printing a number of records in a while loop?

I have tried both options, but I cannot perceive any significant change in
performance. Is there a way I can actuall test or predict the usefulness
of using one alternative over the other? I am also using SORT in my sql
queries, so perhaps the db server will have to retrieve all records
beforehand anyways in order to perform the sort. In such a case, I guess
using LIMIT wouldn't make much of a difference. On the other hand, there
are perhaps cases when using LIMIT would make a difference.

Any guidance would be appreciated to solving this problem.
Thanks in advance,
Marc