All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
Praying in the mosque is better than praying in that room for two reasons: the first is that the congregation is mostly bigger in the mosque. The Prophet, sallallahu ‘alayhi wa sallam, said, "A man's prayer with another man yields a greater reward than his prayer individually. And a man's prayer with two men is greater in reward than his prayer with one man; and what is more is more beloved to Allah, the Almighty." [Abu Daawood and An-Nasaa'i - Ibn Hibbaan graded it Saheeh (sound)]
The second reason is that the mosque is farther away; the Prophet, sallallahu ‘alayhi wa sallam, said, "The people who get the greatest reward for prayer are those who walk the farthest to it, then the next farthest." [Al-Bukhaari and Muslim] Ibn Rajab wrote, "This hadeeth as well indicates the virtue of walking to the mosque from a far place, and that the farther the mosque is, the greater the reward..." [Fat-h Al-Baari]
The Hanbali book Ar-Rawdh Al-Murbi‘ reads, "Performing the prayer in the farthest of the two mosques is better whether they are old or new or not and whether the number of worshipers in them differ or not. The Prophet, sallallahu ‘alayhi wa sallam, said, 'The people who get the greatest reward for the prayer are those who walk the farthest to it, then the next farthest.'"
Moreover, if this room is prepared for prayer and the owner has not offered it as a Waqf (endowment) to be a mosque on a permanent basis, it is not considered a mosque and the rulings relevant to mosques do not apply to it. Accordingly, praying in the endowed mosque is better given the great merits earned by attending the prayer in the mosque, and this also helps keep away from the scholarly difference of opinion pertaining to the obligation of attending the congregational prayers at the mosque.
Ibn ʻUthaymeen said about the difference between the mosque and the prayer room (Musalla):
"A mosque is a place that has been designated for offering the prayers (on a permanent basis and it is known that it has been set up specifically for that purpose). It is offered as a Waqf and cannot be sold or disposed of ... A prayer room, on the other hand, is a place that may be used for prayer or not, and it may be sold along with the property in which it is located ... Accordingly, the religious rulings that apply to them differ. With mosques, the person who enters them is required to perform the two-rakʻah (unit of prayer) prayer of greeting the mosque; the menstruating woman cannot stay therein, nor the person in a state of Janaabah (state of major ritual impurity) except after ablution; and it is impermissible to buy and sell inside it. All this does not apply to the prayer room."
Allah knows best.