The Ibn Ezra (8:24) reconciles these contradictory verses by proposing that the age of twenty five was appropriate only for the work of the tent (עבודת אוהל) whereas thirty was appropriate for carrying the equipment (עבודת משא). The Ibn Ezra doesn't elaborate on the subject and leaves us wondering as to what constitutes עבודת אוהל?
The interpretation of the Rashbam (ibid) may shed some light on this ambiguity (note that the Rashbam does not address the Ibn Ezra here, but gives his own interpretation, however it is possible that he saw his commentary and was influenced by him). According to him, the age of twenty five was appropriate for guarding the Mishkan (משמרת המשכן) only. When the Levite reached the age of thirty he was eligible for עבודת משא as well.
Alternatively the Ramban explains that a Levite at the age of twenty five was eligible for עבודת משא as well. This is evident from the Parsha (8:24) where עבודת משא is clearly included within the duties of the Levite, thus refuting the interpretation of the Ibn Ezra. Rather the Parsha in Behalotecha (8:24) is teaching us that the Levite is not able to become an overseer (פקיד ונגיד) until he reaches the age of thirty. The reason for this is explained by the Ramban (8:24)
והטעם בזה, כי כל אדם נותן לבו בעשרותיו, כי ישתנו בהן הטבעים וידע
או לשלשים, כי ידעו בו שכניו וקרוביו ואביו ואמו וילדיו ויודיעוהו, אבל
בהגיעו לכ"ה לא ירגישו בו כל כך, ולכן לא צוה למשה שיטרח למנות רק מבן
שלשים שהאיש נודע בהן
He goes on to explain that the reason why in the first temple they included Levites that were only twenty years old (1 Divrei hayumim 23:24-28), is because since there was no more carrying to be done as in the times of the Mishkan (only those chores enumerated in 1 Divrei hayumim 23:24-28) even the young Levites (from the age of twenty and on) were eligible for it.