Personally I always do Thameslink as it also brings you out nearer to the EMR platforms than the underground does.
As per previous posts, vertically yes, you are directly underneath, but in walking terms I don't think there is much difference. It can take awhile to get from the Thameslink platform to the barriers, particularly if the way out is still congested by passengers off the previous train, and then you have to walk a far distance down the congested lower concourse to get to the escalators (assuming that they are in service), and then back along the upper concourse to the EMR platforms.
Whereas if you stand in the right place on a Met train, you can be up the stairs and through the barriers in a few seconds. Up past the travel centre into St Pancras proper (the only bit that occasionally suffers congestion) and up the stairs to the deserted upper concourse, and you can quickly get to the EMR platforms.
I will admit that it is a slightly longer walking route, but it is much less congested, and you don't run the risk of finding one or even both the up escalators out of action. Unfortunately I have been caught too many times by congestion getting out of Thameslink, or by the escalators being out of action, that I now always use the underground in preference to Thameslink.