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.

Hi what bothers you more? 
To my visual sense, lower eyelid fat bag can have a more profound effect to the overall facial expression in a negative sense, which can be seen even from across the room... fine wrinkle is exactly that and I can’t imagine having too much negative impact to the overall facial appearance, especially at your age.
I perform many lower eyelid surgeries every week, and roughly half of my cases are revision surgeries from lack of adequate fat bag removal done elsewhere. When I ask the patients why they did the first surgery, the purpose was to “remove some fat bag and tighten the fine wrinkles by lifting up the skin”... as other experts have alluded to, excising and lifting will take away excess skin but will not get rid of fine wrinkles...  at your age of 31, I can’t imagine excess skin under your eyelids... infact, we rarely excise any skin till age 40 to even 45 now a days, and take the fat bag out exclusively via trans-conjunctival approach, thereby saving the patients any visible incision line.  
I can’t be sure until seeing some pictures of your eyes, but my typical menu for my 31 year old patients with early fat bags formation is removal of fat bag through trans-conjunctival approach, and Botox to the inevitable beginning of crow’s-feet laterally which is more often the case than obvious under eye wrinkles.
If however main goal is to treat the fine wrinkles, (either exclusively or in addition to removal of fatbag through a sound surgical technique), you would need to tighten the collagen in your skin and Erbium laser, TCA chemical peel, and most recently Ultherapy have all proven beneficial to certain degree and each carry their own potential benefits and risks depending on your skin color and ethnicity. I hope this helped you and good luck!

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

The aged appearance of undereyelid skin may be related to wrinkles and poor texture, excess skin and bags. The bags usually need surgery to remove or reposition the fat pads. Some bags are fluid accumulation and surgery doesn't help these festoons. Poor texture is treated by resurfacing with chemical peels or lasers such as fractional ablative carbon dioxide (Fraxel Repair). Excess skin is usually treated by surgery but some patients achieve significant tightening by Fraxel Repair and/or Thermage radiofrequency tightening.

For so many 31 year olds, we are now treating the under eyes with Restylane avoiding the need to perform lower eyelid surgery. You might consider this option.
Regarding the two options you have been given, I personally think it is wrong to make my patients practice medicine. This is what you are being asked to do in choosing which approach is right for you. I think it is unlikely that the Erbium laser treatment will iron out your lower eyelid wrinkles. Erbium resurfacing is not as damaging as CO2 but it is also not nearly as effective. In general it is better to under treat than over treat but it is not fair to subject people to treatments that have almost no hope of achieving the desired goal.
You description of the proposed surgery is also a little vague. If the doc is proposing to cut your lower eyelid skin, remove fat and skin, you should thank that person for their time and move on. It doesn't matter if he or she did a great boob job on your best friend. Go find yourself a different surgeon. I would suggest looking for an eyelid plastic surgeon with a cosmetic surgery orientation.
Check the ASOPRS website (ASOPRS.org). The site has a directory by zip code. Check the surgeon's website and make sure they offer cosmetic surgery. You are also welcome to fiy out to LA and have a free consultation in my office.

It sounds like you have two issues. First, the lower lid wrinkles. This can be addressed with surgery or with laser. It all depends on how much loose skin you have and the integrity of your lower lid support. Second, the lower lid bags. This is most likely due to herniating fat, which requires surgery to remove. Sometimes a combination of surgery and laser is most effective. You can have the fat removed from the inside of your eyelid to hide the incisions and then have laser resurfacing on the skin to tighten it up. I hope this is helpful. Good luck.