Let's try a little math. The EnergyStar requirements for computer monitors require that the monitors use 2W or less in sleep mode and 1W or less in "off" mode.
http/www.energystar.gov
Given that I haven't seen many non-EnergyStar qualified displays in the last 8 years, I'm going to use that for my basis.
Let's assume the monitor is actually used 10 hours per week. That means it's asleep 158hr/wk. 158 * 52 wk/yr * 2Wh = 16432Wh = 16.5KWh max
We pay fairly high electric rates in Texas, let's call it USD $0.16/KWh. 16.5KWh * $0.16 = $2.64 US per year, or 1.77 Euro/yr at today's exchange rate. That's for a "consumer", which for argument sake I've made a home user who uses the computer very little.
Businesses will save even less. In a typical business, the in-use time is 45-50 hr/wk, meaning only about 120hr/wk in sleep/off, and most businesses pay slightly lower electric rates. 120 hr/wk * 52 wk * 2Wh = 12480Wh = 12.5KWh * $0.15/KWh = USD $1.88/yr = 1.26 Euro.
So, yes, this could save you a bit, but "several Euro" per year would require electric rates of around USD 0.27/KWh, and that's assuming your monitor draws the maximum allowed in sleep mode and that you don't use your monitor very much.
I'm all for energy efficiency (I look for and buy products that meet my needs and are energy efficient and have for 10+ years), and every little bit helps, but they're stretching a bit on this one. More hype than savings on this one, if you ask me. If they can offer this for less than about $2.50 additional cost at retail, it will have some return on investment.