The stock LA350 comes with two loops or tuning elements: one for
3-9mhz and one for 9-30mhz. It does not come with a MW element, but
you can buy one separately, if you like. Universal has them
(http://www.universal-radio.com/catalog/sw_ant/1806.html).
If you DID buy the MW element already and the antenna's performance is
still poor, I'm surprised. I never use the LA350 for MW, but have
always been happy with its performance on SW.
I notice you said the antenna works better on MW with the Drake. The
LA350 produces a good bit of gain. I'm not sure where you are or what
your listening conditions are, but it's possible that you need to use
the attenuator on your 2010. When I used the LA350 with an SW77, I
almost always had to have the attenuator in play.