Good question. I assume that by "deep chemical peel" you mean a Baker-Gordon phenol peel or a Hetter formula variation. Phenol peels can take a long time to fully recover. You are looking at swelling and peeling for a week followed by redness and sensitivity of at least a month. Depending on your skin type, you may stay pink for quite some time after that (I personally had one patient have some degree of pinkness up to 4 months). In regards to a lower face/neck lift, recovery can be much quicker, after two weeks you can go out and go about your day, with full exercise activity and no restrictions at 3-4 weeks depending on how you heal. So, long story short, it really depends on what you are looking to achieve and what your skin type is. If you were considering one vs. the other, really speak with your surgeon and discuss what your concerns are and what your goals are. Often times the optimal treatment needs to be "two staged", however that does double the recovery time and downtime. But being able to adequately communicate with your surgeon will give them a better idea of which direction to guide you in. I hope this helps!