敬请 + ([person]) + [two-syllable verb]
恳请 + ([person]) + [verb phrase]
敬请 and 恳请 are 请 with respect added: 敬 "respectfully", 恳 "earnestly". They go before the verb in invitations, notices, announcements and formal letters, where a bare 请 would sound too plain.
敬请 addresses readers, guests or customers. The verb after it is a set, two-syllable one: 光临 "attend", 期待 "look forward to it", 谅解 "understand", 关注 "follow", 留意 "take note".
恳请 is stronger and more personal. It asks for something the writer really needs – support, forgiveness, correction – and can name who is being asked.
The verb after 敬请 or 恳请 has to match its register. Spoken verbs and softeners like 一下 don't fit.