Are you referring to the axe only, or the combo telescopic axe/pole?
My two cents....Ice axes are great for what they are designed to do....moderate ascension on lower angle snow/ice/neve where you are either kicking steps or using crampons, or as a safety precaution while descending, and using it in "self arrest mode". Familiarize yourself with that technique and practice it if possible if you have not already. Plenty of people bite the dust sliding down a snowfield then into a boulder field or crevasse. It is amazing how fast you can get going on low angle, hard, frozen snow. Also amazing how fast you can descend (controlled) by glissading down a snow field.
I have used both ice axes and trekking poles extensively (too much climbing in US and Canada!), and would say neither does both things well.
If you are in glaciated areas, climbing up snow chutes or crossing angled snowfields, use the ice axe, especially if a slip would prove dangerous/fatal (for self arrest mode). For the rest of the steep hiking, side-hilling, etc. that is not on snow, I would opt for the poles.
Also, if you are needing a good reliable ice axe, take a look at Grivel GZERO Axe or the CAMP Corsa (either one in 60cm length range would be fine.) They are nice and light. Pair it up with a
tether like THIS. That way, you can switch from left to right hand easily, as the clip is in the head of the axe, vs. around your wrist. Attach it to your backpack's waistbelt so you don't drop it. If you are in terrain that requires roping up (glacier travel comes to mind) you would then attach it to your harness.
Hope this helps!