In the first case of its kind, the ASA upheld a complaint by Birmingham College of Food, Tourism and Creative Studies against Clarendon College.
Birmingham based its case on grades in inspection reports on the two institutions, which it said showed it performed best.
The ASA's judgment on the squabble has forced Clarendon to discontinue a leaflet containing its claim. It was issued just as a self-evaluation report from the Further Education Funding Council's inspectorate reveals colleges are increasingly clashing over the use of inspection reports for marketing.
But, though the inspectors acknowledge the use of reports in advertising can be "contentious", they leave it to the sector to resolve such disputes itself.
Birmingham College, which was awarded nine grade 1s and four grade 2s by inspectors, lodged its complaint last February after Clarendon (11 grade 1s, six 2s and two 3s) had refused a request to withdraw promotional literature.
Birmingham principal Eddie McIntyre said: "The governors, students and staff of the college had worked very hard to achieve the inspection result that showed that we are clearly, by any measure, the best college in the country and we did not want that hard work undermined by a usurper."
In a statement, Clarendon pointed out that the claim was made in only one of its promotional leaflets. A spokeswoman insisted Birmingham was a specialist institution, and therefore had no place in the general FE league. She added: "A single complaint from a Birmingham college has resulted in the ASA's judgment. There are 452 FE colleges in England and Wales."
The FEFC inspectorate's progress report finds that "inspection is well received by colleges", though it acknowledges almost a fifth of those inspected have made written challenges over grades. Inspectors have agreed to changes in 10 cases - 0.5 per cent of all the grades awarded.