Modified duration should always be less than Macaulay duration since:
Modified = Macaulay / [1+ (YTM/n)] where n= number of coupon periods in a year. However, they will be very close. The difference between the two is that Macaulay duration assumes that bond cash flows are fixed. Modified duration does not make this assumption so it can also be applied to bonds with variable cash flows.
I dont think the statement u gave about modified durations and cash flows is correct.
Macaulay Duration does not consider the fact that duration does NOT remain constant and duration changes with level of YTM rates. So,modified duration is computed.
"The concept of modified duration can be applied to interest-rate sensitive instruments with non-fixed cash flows, and can thus be applied to a wider range of instruments than can Macaulay duration. Modified duration is used more than Macaulay duration."