It depends on your purpose.
Last-Modified will mean that the server is happy for you to keep using an entity that had the same last-modified value (or later by implication, though it would be strange for the server's last-modified to ever go back, but could happen in some multi-server situations).
E-tag is stronger (all the more if it's not a "weak" e-tag) in that it identifies the specific entity (e-tags for different language versions, different content-type versions, or different content-encoding versions will differ unless they are actually the same entity [which can happen, in a restricted set of circumstances]).
Both can be "loose" in terms of perhaps a server change is considered insignificant; the server is happy for you to keep using the previous entity because it considers it the same (except "strong" e-tags, which must indicate octet-to-octet identity for use with range requests).
Both can of course just be plain wrong. Bugs happen. That said, when they are wrong its more often in the other direction, reporting a change when none has happened (a valid behaviour, one is allowed to be over-cautious about freshness; it never damages only makes sub-optimal).
The question then, is whether you need to know that the server considers no change to have been made (most usage) or there really has been a change (pretty much restricted to diagnostic tools).
Unless you've a clear reason not to, trust last-modified and e-tag (but trust e-tag more).