In their typical use, Winsteps and Amos do different things.  Winsteps fits the Rasch IRT model to data. The Rasch model only models each item's difficulty. It assumes each item's loading on the underlying factor is identical. Amos fits factor analytic models which generally don't estimate difficulty at all and which are focused on estimating the factor loadings of individual items. You might be able to fit mean and covariance structural models (i.e., MACS; CFA models with thresholds) in Amos, but that would still be fairly different than the Rash model.

Rasch has a surprisingly irrational, brainwashed, cult-like following. So, Raschians will tell you to always use the Rasch model. Their solution would be to use Winsteps for both the pilot and full sample analyses. And this will probably work fine if the items are from a source of known quality.

However, if by "pilot" you are implying that this is the first analysis of these items or the first application in your population, then I think applying the Rasch model to exploratory data is really really stupid. The Rasch model assumes that all the items have equal loading on the underlying factor and in exploratory settings you have absolutely no justification for this very big assumption (you should assume the opposite, which would always preclude a Rasch analysis). But, as I said, Raschians feel really strongly about the Rasch being the only way to analyze data and they don't seem to worry about violated assumptions or lack of fit (or bothering to check for violated assumptions or model-data fit).

I would recommend that you use a model that allows the factor loadings to vary (like the 3PL or any factor analysis model). If Amos cannot fit the pilot data because they are too few, I would use classical test theory (CTT) or I would apply IRT using stronger Bayesian priors on the item parameters (using an R package like ltrm, or BILOG, or IRTPro). Using CTT would be very easy: Just calculate the means of the scored items. These means will correlate > 0.90 with the item difficulties that you obtain from an IRT analysis or thresholds from a MACS CFA model.

Thank prof Alan Mead for the clarification