I would use the bass clef for the lower thirds in your passage. Three ledger lines above the bass clef (and three below the treble) are quite common in music. It all comes down to what's easiest to read. In your first, I have to mentally break the notes apart, and I don't have to in your second so the reading is automatic. The second passage is easier to sight read.
For some ideas, have a look at Brahms' Intermezzi, in particular Op. 117 No. 2 (which you can find here. It has a lot of broken chord passages in the left hand, that run well up into the treble clef and back down to the low notes. You'll see that he doesn't have any hard and fast rules about which clef he puts notes in; rather, he has them in whichever clef is easiest to read. If you study this, you should begin to see reasons that he chooses one over the other.