They are two different models and therefore could legitimately come up with different answers. This seems particularly if the data are unbalanced (e.g., if time and approach are confounded). Another possibility is that the two-way analysis drops cases because of imbalance - and hence has less information and more bias (though there are ways round that using multilevel models etc.).

For starters, in your 2x2 ANOVA, are you incorporating repeated measures into the model by treating "individual" as a random effect? You should be doing so. If you are, that could explain some differences.

However, if the first model (pooling all of the data) did not include time at all, you might be missing the actual data that is causing a significant result. For example, if there was a difference in sampling time across your treatment groups, then you might not be able to assess whether it was your collection method or time that caused the effect. As it turns out, once you have included collection method AND time (the latter of which would seemingly disappear if you pooled all the data), time appears to explain more variation in the data than the collection method. 

Just to elaborate on Brent's point - repeated measures analyses would treat the individuals as a random factor. Typically this would increase sensitivity to the collection method factor (because T1 and T2 would be positively correlated and the variance accounting for this correlation is partitioned out of the error term). This makes me think that there may be missing data (though it is also possible that T1 and T2 are negatively correlated - but that is less common).

An alternative to this design is an ANCOVA with T1 used as a covariate and change from T1 as the DV. This removes the repeated measures component and is generally slightly more powerful (though it tests a slightly different, albeit slightly more plausible hypothesis).

Agreed with Thom's previous points (looks like our initial answers were at the same time and essentially saying the same thing - that your data might be confounded).

Thom - It seems the ANCOVA approach would only work if you have two points in time that are being measured. Hence, you have the T1 used as a covariate (initial measurement) and the change from T1 as the DV (final measurement). If there were multiple measurements made (3 or more), it seems either impossible or that the ANCOVA would get very complicated, very fast. Correct me if I'm wrong though. Just curious as to how that could work.

You can generalise the ANCOVA approach to multiple time points using change scores for T2 to Tk as a factor. It isn't too tricky - though it is sensible in all these models to centre the covariates.

Thanks Brent and Thom for both of your responses.  I had 8 different time stamps with at least 3 of them be 'significantly different' to others, both high and low and 3 different capture approaches.  Just based on a visual assessment of means with 95%CIs shows similar hormone levels between capture approaches within each time period but variability was greatest across time.  I did treat the data as a repeat measures as the same individuals were being used. I dropped any individual from the analysis that I did not have all 8 samples collected so this did leave one group as being uneven... With this in mind is it best to disregard the pooled results as I think time has played a more significant role than capture approach?

The repeated measures analysis is superior but you are biasing the results by dropping cases (and losing power). I'd suggest running the analysis as a multilevel model (aka linear mixed model) and trying to retain all the cases. In the case of perfect balance the multilevel model would be equivalent to the ANOVA (assuming sphericity).