Is performing ablution at home before going to the mosque for congregational prayer more virtuous than doing so at the mosque, and is there a hadith on this?

Summary

Several hadiths with differing wordings indicate the merit of purifying oneself at home before walking to the mosque for an obligatory prayer, and the fatwa concludes that this virtue is established from the Prophet. According to Sheikh al-Shanqiti, the virtue also covers anyone who performs ablution right after the call to prayer, whether at home, at work or elsewhere, and then hurries to the mosque. Those whose ablution is nullified on the way still gain the virtue because they intended a good deed. The fatwa also notes the merit of promptly answering the call to prayer and the possible saving on mosque water bills.

Written in our own words from the original fatwa — check the source before acting on it.