Here's one more thing that pops into my mind which undermines my argument above, but supports the assumption that Michael trusted Clemenza more.
When Tessio says he knows the restaurant, Michael wants Clemenza "to figure a way to have a weapon planted there". Why Clemenza? After all it was Tessio who knew the bar!
Was Tessio too dumb in technical ways?
Or was it that Tessio's men were known in that bar?