No matter what you do you'll be finding yourself on plenty of conventional roads between Lubbock and Laredo, so I feel like you'll get a good dose of those whether you do I-27 or not. Personally, I find conventional roads to be nothing special, especially in an area like the Texas panhandle without much in the way of scenery to speak of (it's going to be a bit of a letdown after having done US-550 a few days before). Since you will be passing through a couple dozen small towns en route to Laredo, chances are you won't really have much of a chance to really explore any of them in depth and still make good time, so they mostly will exist as obstacles to cost you time. My opinion, anyway. I usually go through an area on Interstates the first time and then resort to conventional roads when I've had my fill of that particular stretch of Interstate.
Texas can be pretty exhausting to drive through, so I wouldn't begrudge you for wanting to just get out of the state ASAP for a change in scenery (though you may find yourself missing TxDOT by the time you get a feel for what ODOT has to...erm...offer.) If you do decide to clinch I-14, and if you're into county counting, take note that it's only a few minutes from the west end of I-14 to the Lampasas County line. I kicked myself when I was logging I-14 in TM and realized how close I was to getting another county.