Whether to have a screen with target ID's or not is one of those things that boils down to personal preference. Some people use the ID number whilst others will just go off the tones despite having the ID's. You soon learn that often the tones offer a better idea of what is under the coil than heavily relying on the ID numbers, which can become more inaccurate the deeper the target is.
This is especially evident on the Tesoro which only gives off a single tone, but you will soon learn that despite only having a single tone (as do some of the more expensive tesoro models) it still carries a fair bit of information regarding the depth of the target, and the type of metal being detected - something that can only be gained with a decent number of hours testing in-ground targets. The Compadre carries the same discrimination circuit as on much more expensive detectors in the Tesoro range, so they certainly haven't skimped in that area.
Best to give one or the other a try, and if you don't warm to that particular detector, you can always sell it and try something else to see what suits. I went though a few detectors before eventually finding one that suits my requirements, but the only way to find out is to physically get out there and give your chosen detector a good workout.
Here are the instruction manuals for both detectors to help you make a more informed decision on what you are after. Please note when when you click on the link for the Eurotek, it is a direct download for the instruction manual PDF. It is evident from the length of the instruction manuals on how simple the compadre is to operate vs the Eurotek, though if you like to have a detector with more adjustability and features, the Eurotek might be more attractive, though a bit more complicated to setup/operate. There is no denying that the Eurotek has a lot of useful features for its price, also the advantage of being able to use different coils may be an added plus.
Teknetics Eurotek
https://www.google.com.au/url?sa=t&...wQFjAA&usg=AFQjCNHW18vboNdHurpuYqxBmguhW8F9NQ
Tesoro Compadre
http://www.tesoro.com/info/manuals/current/compadre/compadremanual.html
Here's another site with some user reviews of the compadre vs the slightly more expensive Eurotek Pro. Do note that the depth capability of the Compadre is less on this comparison due to running the smaller 5 & 3/4 inch coil vs the optional larger 8" coil version, and despite what it says, the coil is fixed and cannot be interchanged with others. The compadre runs a higher frequency than the Eurotek (12kHz vs 7.81), and hence is also noted as being quite sensitive on small gold jewellery items.
Also have a look at as many you tube clips as you can on both detectors being used in the field, this will give you a better idea of what they are like to operate in the real world vs the usual bench top air testing of coins.
http://metaldetectorreviews.net/detectors/compare.php?x=341&y=31