If it were me and I wanted my hair straight then I would go with a relaxer. Reason being is that the results are more predictable IMO and there is a lot of information out there about caring for relaxed hair.
The newer smoothing treatments leave some people with curls still, they wear off, and it seems like some stylists dont even have all the info about the product.
I agree with Dusalocs, that it's important to look at reviews for whatever stylist you're considering. Make sure they base your scalp with something to protect it and if you go for touch ups they shouldn't reapply the relaxer to hair that isn't new growth.
I really like your curls, but because you're a guy at least the grow out wont be too tough if you decide you want them back.
With a relaxer you can probably wrap your hair to get it smooth and also give it that flippy look. I used to do that when I was relaxed and I always had skater hair the first day lol