Is it better to Daven [pray] with a earlier large minyan or better to wait to daven later with a much smaller minyan where I will be needed as the tenth?
Ken, great point.
There's some discussion about if you choose between doing a mitzvah in an "okay" way sooner, vs. a "better" way later. (E.g. we wait till Saturday night for Kiddush Levana so we're in a more spiritual mood when we say it, having just gone through Shabbos; even though earliest time for Kiddush Levana may have been a few days earlier.)
Classically in Halacha it's considered "davening better" when doing it with a larger crowd, but that assumes the later people will still have their minyan. I agree, if you can daven earlier and then attend later, that's ideal.
This is a quotation from an an excellent article on the subject found at the OU Kosher web site.
The idea from Rav Auerbach seems to be that making the minyan takes precedent.
Sometimes halachah dictates missing tefillah betzibbur. If one arrives late to shul and realizes that by starting Shemoneh Esrei of Minchah he will not finish in time for Kedushah, he should not start (SA, OC 109:1; MB 109:2). However, if one is a “slow davener” and regularly does not finish Shemoneh Esrei in time for Kedushah, many authorities advise that he start Shemoneh Esrei with the congregation—thereby benefiting from tefillah betzibbur—and daven at his usual relaxed pace, even though it will mean missing Kedushah (Ishei Yisrael 33:4 and note 25).
Other priorities sometimes overshadow tefillah betzibbur. Even though six daveners and four others who have already davened constitute a minyan (and can therefore respond to Kedushah, et cetera) but are not eligible for tefillah betzibbur, Rav Auerbach rules that one should still be part of those six and help make a minyan even if he thereby forfeits having tefillah betzibbur elsewhere (Halichot Shlomo 5:8). Similarly, he rules that a group of frum soldiers should forfeit tefillah betzibbur on Rosh Hashanah in order to spread out to other bases to blow the shofar for those who would otherwise not fulfill this mitzvah (ibid., note 28). He also rules that a soldier who has guard duty on Shabbat should not switch it so that he could daven with a minyan if by doing so his replacement will violate Shabbat (ibid., 5:6). In other words, certain mitzvot, like strengthening a “weak” minyan, blowing shofar for others and preventing another person’s desecration of Shabbat override tefillah betzibbur.
The Mishnah Berurah (236:14) rules that it is better to daven Minchah privately rather than do so with a minyan after sunset. In a similar vein, Rav Yosef Dov Soloveitchik, following his grandfather, rules that it is preferable to daven privately rather than do so with a minyan that recites Shema and its berachot after the proper time.