If the comparison you are performing is in Crystal Reports, then you can use the Crystal Reports Date function:
Date( {datetime expression} ).
If you are trying to do this in ASA, ASA has a similar Date function.
ASE may also support a similar function but I don't know for sure as I haven't used it enough to remember.
Either of these methods are probably more efficient than converting to varchar because it allows for a numeric comparison rather than a string comparison.
If your logic is being used in a WHERE clause, and you want it to take advantage of indexing, you'll need to use a compound logical expression. The following example would be capable of using an index on MyTimestamp1 if it existed:
WHERE
MyTimestamp1 >= Date(MyTimestamp2)
and
MyTimestamp1 < Date(MyTimestamp2 + 1)