Blepharoplasty Vs. Laser Resurfacing for Under Eye Lines?

If you have under eye bags, then the fatty tissues have to be addressed surgically. And sculpting the fat from the inside of the eyelid(transconjunctival blepharoplasty) is a good approach. Erbium/CO2 resurfacing will help the fine wrinkles, but not the fatty under eye bags.
The standard blepharoplasty which removes fat and skin under the eyelash line(subciliary) is also a popular way to tighten the bags without a laser.
I would recommend to discuss with a plastic surgeon who performs many eyelid surgeries as to which technique fits your needs.

A variety of treatment options are currently available for the treatment of lower eyelid aging. The specific treatment chosen needs to be individualized based upon the patient's anatomic findings and aesthetic goals. Although your clinical history is helpful, it's virtually impossible to make a specific recommendation without pictures or a physical examination.Laser re-surfacing of the lower eyelids provides excellent results when patients present with poor skin quality with associated fine wrinkles. Under these circumstances, this approach can significantly rejuvenate the lower eyelids.Unfortunately, when excess skin or fat pads are present, more aggressive treatment modalities are often necessary. Under these circumstances, blepharoplasty surgery is usually necessary to remove excess skin and address fat pads. In some cases, a transconjunctival blepharoplasty can be combined with laser re-surfacing to optimize results.In someone who's only 31 and concerned about lower eyelid surgery, it's essential to consult a board certified plastic surgeon with experience performing this type of procedure. This surgeon should be able to formulate a treatment plan that addresses your age, anatomic findings and aesthetic goals.

Surgery will correct the "eye bags", but fine wrinkling will need to be addressed another way.  Procedures to consider range from topical medical-grade skincare to botox or RF skin tightening to CO2 skin resurfacing or a combination of two. A proper recommendation can be given by a reputable and experienced board-certified facial plastic surgeon who is able to evaluate the area for you while taking your desired outcome and cost into consideration.

If there are fats bags herniating forward, then a blepharoplasty is required to remove the fat. If the overlying skin is loose or wrinkly, the addition of laser skin resurfacing is great at smoothing out the skin and making the overall appearance much nicer. This combination approach is often very satisfying to patients. 

Laser or chemical peel does a good job of smoothing out fine lines.  The only problem is that there will be several weeks of redness and you will need to cover that with makeup for a while.  Also, the lines will eventually return over time.

Recent research reveals fat herniation is due to a proliferation of orbital fat, not a weakness of the orbital septum, skin, or muscles as we all assumed in the past.  That is why attempts to remove bags by laser tightening have failed the test of time.  Laser may soften fine lines and can be used in conjunction with blepharoplasty.  Best wishes. Knowledge is power.  Luis F. Villar MD FACS