Academic work on curve inversion generally favours 3m10s over twos-tens, because the 3-month bill tracks the actual policy rate almost exactly rather than embedding expectations. When 3m10s inverts, long-term investors are accepting less than the risk-free overnight rate to lock money up for a decade.
It inverts later than 2s10s and un-inverts later too, so the two spreads can send conflicting signals for months.
Example: the 3-month bill yields 5.35% and the 10-year 4.15%. 3m10s is -120 bp, a deep inversion, while 2s10s may already be back near zero.
Related: twos-tens, inverted-yield-curve