Some answers, from a chaburah I wrote up a few years back. (I didn't write down the precise locations of the sources - will have to look them up when I have some time.)
Radvaz notes that by מקרא ביכורים the expression is אשר נשבעת לאבותינו לתת לנו, which can be understood as נשבעת לאבותינו – to Avraham – and therefore לתת לנו, it pertains to the whole Jewish people, gerim included. Whereas by וידוי מעשר the expression is אשר נתת לנו, and it wasn’t given to the gerim; כאשר נשבעת לאבותינו there refers to זבת חלב ודבש.
Mishneh Lamelech quotes R. Moshe ibn Chaviv, who points out that Yechezkel states that gerim will get a portion in Eretz Yisrael in Moshiach’s times; therefore they can well say לתת לנו in future tense. (A logical reason for this is that gerim who joined the Jewish people after Yetzias Mitzrayim, when we were at the highest heights, may not have been totally sincere; not so with those who became gerim during the years of galus.) Whereas אשר נתת לנו is in past tense.
A couple of mefarshim on Rambam bring an idea from R. Shmuel Primo, that the expression ארץ זבת חלב ודבש is never found in Chumash Bereishis (addressed to the Avos), only in Shemos (addressed to the Jews in Egypt) and afterwards. So if in וידוי מעשר the expression כאשר נשבעת לאבותינו refers to ארץ זבת חלב ודבש, then אבותינו there necessarily means the Jews who were in Egypt – and the ger isn’t descended from them.
Yet another answer, from Mirkeves Hamishneh, is that מקרא ביכורים must be said in lashon hakodesh, and there אבותינו can mean “masters” (as in וישימני לאב לפרעה); whereas וידוי מעשר can be said in any language, and in other languages “av” means only “father.”