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How technical? Each has different bandwidth overheads.
From a practical standpoint, if you're obtaining a GigEtherent handoff with (say) 150 Mbps of contracted bandwidth vs. your STM1's 155 Mbps, you probably want to shape for the contracted rate. Generally, it would be difficult to see much of an effective bandwidth difference if the GigEthernet is rate-limited to such a similar value as the STM1. However, often the contracted bandwidth, on the GigEthernet, can be easily and quickly changed.
One subtle difference, equipment that supports STM interfaces is more likely to offer extensive QoS features than equipment that supports Ethernet interfaces which can be especially important for WANs.