Tiburtina station after the renovation in the 2011 is quiet and pleasant. Quite a difference compared to the crowd of Termini.
From Tiburtina the metro line B runs no stop (among others) to Colosseo and Fori Imperiali (€ 1,50).
For the Spagna stop, instead, a change to the A line at Termini is necessary.

This makes the choice between Termini/Tiburtina just related to personal interests and hotel area, since the difference in commuting time is minimal.
I would pick the least expensive train fare, which in my experience is always Italotreno. Add that wifi is reliable, the service excellent and the staff young, cordial and keen to help. A far cry from the unpleasant and grumpy Trenitalia employees of the old days.