Do both. SRV, Philip Sayce, Richie Kotzen and a host of others are good at this. Comp the rhythm chords and when you are changing chords once in a while throw in a short lead type phrase. A lot of trios do this to sound like more than just 3 players. That will give you the best of both worlds.
Otherwise become a slave to the groove. The more you do it the more you'll love it. It helps to not think about anything while you are doing it. Just groove out.