Do I have any control of the transaction?

Not in the same way. The magnetic stripe is dumb and takes no active part in the transaction other than being a source of read-only data. Conversely the chip has intelligence, can establish a secure link with the issuer* and makes the ultimate decision to approve or decline the transaction**. The retailer has some control with floor limits and Terminal Action Codes(TACs), [see: what are terminal action codes?]. Floor limits are no longer hard limited: the nearer to the floor limit the more likely to go on-line. Control effected by TACs is limited.