I have owned the Underdog with a standard core and a variety of stems for a bit more than a month now. It has seen use multiple times daily, and I have experimented with it often in order to get the best results. I have had the E-nano for two days now, but I feel like I am capable of using it pretty effectively already.
My initial impression is that the E-nano seems more professionally/commercially produced whereas the underdog is more of an art piece. Not a rip on either of them, they both have their appeal to me and surely to others. I prefer the sturdiness of the E-nano cord and I like the smoothness of the dial (as well as the fact that it is adjustable straight out of the box of course!), although the thin underdog cord is nice for passing around a table. The e-nano itself seems a bit heavier and possibly sturdier. The core of the E-nano looks sturdier, and the heater tube is made of thicker metal. The nano stems and GonGs seem much sturdier than the underdog's glass pieces. The ends of the nano stems are not cut crookedly like the underdog stems are. Underdog has said that they simply do not have a way to cut the stems better since they order them pre-cut and then polish them in-shop. This is a minor complaint for the UD, but I felt it needed to be pointed out for the sake of the comparison. I like how the e-nano stems have a stop built into them to keep the heater away from the load. The underdog uses a star nut inside of the actual log to accomplish this, and it results in pretty much the same function. The e-nano regular stems are about the same thickness as the thick direct draw underdog stem. The E-nano GonGs are also much thicker than their underdog counterparts. The particular GonGs that I have for my E-nano do not have sandblasted joints, as I would prefer. I will likely sand blast them myself eventually, but it is a pretty minor issue for the time being. Unfortunately, UD does not offer a thick option for GonGs. That said, I really like the Underdog nylon and stainless pieces. I have both the NonG and the nylon direct draw. They seem to work very well in my experience. The E-pick stirring tool is something that I really like as well. It may seem unnecessary but I have been using a paperclip to stir the entire time I have had the UD.
I wish that i had a vvps for the underdog in order to do a more thorough comparison, but currently it will be more of an out of the box type of deal. Feel free to suggest any specific comparison criteria that you would like to see.
After using both logs side-by-side:
The E-nano really does heat up quicker than the UD. I filled the E-nano stems with an amount of bud comparable to what I would use in an Underdog glass stem, but slightly more than what I would use in a stainless NonG. I found that I got best results with a little less bud than I initially used, moving the screen back, and turning up the heat. I get nice, dark, even AVB with this method and it really milks the bong up! I prefer the GonGs, but the straight stem was super tasty. I have found that the nano glass stems fit much more snugly on the heater core than the Underdogs' do. It seems that the Underdog stems allow a bit more fresh air in because of this, but either using a stainless stem or an o-ring on the heater core should help this. I have not had a chance to try the o-ring, but it seems like one should be included in the initial purchase.
I use the underdog by loosely filling a small amount of herb in the stem (whether I am using glass or stainless). I keep the load significantly closer to the heater than I do with the E-nano, since the heater seems to be less powerful. The Underdog does not milk a bong up as well as he E-nano does. This is likely due to the loose-fitting stems when using the glass stems or GonGs, or to the fact that the vape just isn't as hot due to the lack of adjustability. I have found that I can cool-off the UD by hitting it too many times consecutively or when hitting it with friends. This is significant enough to warrant waiting for the vape to regain heat for a nice hit. This could be fixed by using a vvps to up the voltage, but it seems like this shouldn't be necessary.
I believe that the E-nano offers more extraction than the UD with a stock wall wart. It seemed like I got bigger hits with the nano by a considerable margin. The UD is still an excellent vape, but I have a feeling that the E-nano will be the go-to at least until I can get a VVPS for my underdog. I am planning to try some concentrates with the nano as soon as I pick some up from my dude.
As a final statement of comparison, I prefer the E-nano. It seems like the E-nano is more ready to go straight from the box since it is adjustable and the stems fit well right away. These problems can be remedied with the Underdog, but I personally would prefer to not need to remedy them. The Underdog is absolutely a respectable vaporizer, and in my opinion a more aesthetically pleasing one than the E-nano. The underdog also has the advantage of more accessories and stems with an initial purchase than does an e-nano. The nano performs better for me in vapor production and complete extraction, and I also prefer the design. These are the three main reasons why I prefer the nano to the Underdog.
EDIT: After further comparison, I still stand behind my analysis above. I do tend to like a vape that is slightly towards the hotter end of the spectrum, so maybe my underdog just doesn't run very hot compared to most. I hear of some people scorching herb with their UD, but I have never even come close to this happening. Anyone who suggests that I do not have adequate experience with the Underdog is incorrect. I have been using it for a while now and have tweaked every variable possible. The E-nano is still my preferred vape.