Iron Dome was designed to intercept cheap artillery rockets. Think of those as home made Grad rockets. It will be useless against Shaheds or cruise missiles. The Shaheds and cruise missiles can change direction unlike artillery rockets. In order to protect from air attacks, Israel has multiple layered air defense systems. Iron Dome is just one of those systems. They also have David's Sling for intercepting aircraft, which is what you would use against Shaheds or cruise missiles, and Arrow for intercepting ballistic missiles. David's Sling would likely work against those kinds of weapons but it is too expensive to use against a Shahed. Each interceptor missile of David's Sling costs over a million dollars.
I disagree. The Iron Dome is more than capable of intercepting Shaheds and Cruise Missiles - with a caveat.
The Tamir interceptor within the Iron Dome system is similarly proportioned to a WVRAAM. It is a maneuvering missile with mid-course correction capability via datalink, a (simpler than AAM) seeker with proximity detonation, It's "simpler" probably because the primary target set is not quite as capable of the active/passive defensive countermeasures of a combat jet.
Shahed and cruise missiles are also not capable of reactive evasive maneuvers. They may have preplanned maneuvers (change of vectors or terminal phase maneuvers) but they are unlikely to be in reaction to an incoming interceptor. In all likelihood - the Tamir, which is touted as an agile interceptor - shouldn't have problems dealing with a UAV/Missile. Further, in 2021, Raphael upgraded the software to deal with this target set and demonstrated the capability in a that included rockets, missiles and UAVs.
That said, where it has a problem is it is Very Short Range. It is really meant to be a "point defense" system and has demonstrated real world effectiveness against direct incoming targets. It probably won't do as well against tangential intercepts of tangoes heading past or away from the firing battery. That will be left to the next layer - the David Sling (DSWS).
I'd say comparing ID to DSWS is like comparing SEA-RAM to SM-2
They're not competitive, they're both capable but complementary.