Old Catholic vs Roman Catholic

Papal Infallibility
Old Catholic: Pope is not infallible
Roman Catholic: Pope is infallible on matters of doctrine

Authority of the Pope
Old Catholic: the Pope is the Bishop of Rome
Roman Catholic: the Pope is the ruling official of the Church

Authority of Bishops
Old Catholic: All Bishops Are equally apostolic
Roman Catholic: All Bishops are under the authority of the Pope

Celibacy
Old Catholic: Not required by clergy
Roman Catholic: Required by clergy

Use of contraception
Old Catholic: Personal choice
Roman Catholic: a serious sin

Sin
Old Catholic: All sin is potentially grave
Roman Catholic: Two types of sin (venial and mortal)

When sin is forgiven
Old Catholic: When acknowledged and asked to be forgiven (prayer)
Roman Catholic: When confessed to a priest and given absolution

Personal confession to a priest
Old Catholic: Not required, but encouraged for spiritual growth and humility
Roman Catholic: Required for sins to be forgiven

Divorce
Old Catholic: It happens
Roman Catholic: Not allowed

Remarriage after divorce
Old Catholic: Yes
Roman Catholic: No

Who may partake of the Eucharist
Old Catholic: All baptized Christians
Roman Catholic: Only Roman Catholics

Number of Sacraments
Old Catholic: Seven
Roman Catholic: Seven

Real Presence of Christ in the Eucharist
Old Catholic: Yes (though not necessarily defined)
Roman Catholic: Yes (through transubstantiation)

Historic Catholic Doctrines
Old Catholic: Yes
Roman Catholic: No–have adopted new doctrines

Catholic Liturgy
Old Catholic: Yes
Roman Catholic: Yes

Athough this is not currently true for the Independent Old Catholic Church, the following is true for many Old Catholic jurisdictions, including the Community Catholic Church of Canada:

Ordination of Women
Old Catholic: Yes
Roman Catholic: No

Holy Orders open to LGBT
Old Catholic: Yes
Roman Catholic: No

Performs same-sex marriage
Old Catholic: Yes
Roman Catholic: No

Open and affirming of LGBT
Old Catholic: Yes
Roman Catholic: No