Investment Strategy roles

I would advise you to take the strategy role - there's a thread on product management/strategy that you can look at, it's pretty recent, to give you a broader sense of how it sits within firms (as a very general matter, of course). I don't know how Europe differs from the US - but as a general rule it's challenging, not impossible, to move towards investments from a strategy role. You can do it certainly - it will take a lot of patience, networking, a CFA wouldn't hurt and absolutely killing it in the role you have. Where you can - I'd try and take on projects that look more like investing than, say, marketing or client service. By way of example, that would be doing more the research, quantitative support for a piece vs. defining the topic, thinking about how it should be positioned across a specific channel, how does it support the growth goals, etc. (though you should also become conversant in that). 

There's no move that won't be challenging, unless you start in the area you want to end in. I could tell you that real estate looks more like fixed income, has more principles than fixed income than, say, equities or whatever - but the reality is that you need to absolutely kill it in your role, prove to others that you are a valuable contributor and eventually earn a shot to leverage your network, social capital and skill set to try a transition. My view is that you should pick the team, firm and culture that you feel meshes best with you to give yourself the best shot.