How do ISPs/Colocation Facilities limit bandwidth for Ethernet Drops?

Usually it's shaping vs. policing - done on the provider's edge interface to you. See here or here for more info.

Shaping buffers traffic above the limit, policing just drops it. I'm guessing your old ISP may have been shaping and the new one is policing.

You could try shaping your side of the interface so your router is doing the buffering to avoid getting to the point where your provider is dropping your packets.

This is a very un-high-tech solution, but one I've seen implemented in place of true QoS and traffic shaping capabilities:

If you want to prevent going over your allotted 10mbps, you could use a CAT3 cable to connect your NIC to the switch.

I saw this used when a small lab wanted to limit a server from flooding their DS3 connection - they wanted to ensure it never used more than a quarter of the bandwidth, so they used a CAT3 cable. Low-tech, but effective.