I think another contributing factor for Tessio's betrayal, could have been wasn't Tessio more of an 'independent' operator than Clemenza
Tessio didn't think much of Michael “Mike, you are wrong” and Tessio may have felt slighted that with Vito gone, Tessio will come under Michael's [the inexperienced boss' kid] thumb

Success! Whilst I acknowledge Clemenza had personal relationship with the Corleones as well unlike Tessio - Both Clemenza and Tessio were disgruntled after the fish tank scene

A side question please, what if Clemenza and Tessio teamed up and conspired together