Not necessarily. A turboprop will burn less fuel than a jet, but depending on the length of the trip the total cost-per-mile (maintenance inclusive) could very well be cheaper in a jet vs. a turboprop due to faster block speeds.

Given European flying (something I have no experience with) there are many issues to consider when picking an airframe: MTOW of the airplane and its fuel burn for ATC and carbon cap-and-trade fees, runway requirements, hangar considerations, availability of training, etc. Also important is the typical mission; if your average stage length is 250nm then a turboprop is your no-brainer airframe; if its upwards of 500nm then perhaps a light jet is the ticket. In this same vein, whats the average passenger load?

The OP is familiar with the CJ1, and the entire CJ family is stupidly cheap to operate for being light jets. Also, I think there is a CJ simulator at FSI Farnborough which makes training easy and a Cessna Citation Service Center at LeBourget which makes service easy. I'm predisposed to like the CJs because I fly one; they're really hard to beat for the blend of speed & efficiency they provide.

Bottom line, there are lots of options out there that could fit your mission...A TBM700/850 if you don't mind a single engine, a C90 or B200, or a CJ1.

Good luck!