I have both, but the rollers have sat unused for nearly two years.
They are different beasts, have differing functions and offer different gains. There are bound to be links I could post on the topic, but I prefer to suck and see for myself.
Rollers: Mine do not offer variable resistance (perhaps some do). They are excellent for smoothing out your riding (direction, pedal technique and overall coordination and fluidity). You can do 'pieces of work' on them, but as on the roads you will be putting some of your effort into staying vertical and straight. There is an initial period (quite long in my case) of acquiring the skills and confidence to use rollers. It is (almost) like learning to ride all over again. Rollers are very good for doing longer, smoother, steady-state pieces - but this can be dull. Worth having a cheap HRM too, as it will may help you to refine your sessions. Setting the thing up to fit your bike is VERY IMPORTANT. If you get the front-wheel roller in the wrong place, it can be tedious and unstable. Have an amusing programme and vary it, or you will end up going mad and eating the wall paper.
Turbo: I have a Tacx Flow, which measures a modest number of data. The great advantage of a Turbo is that you can ride to bursting point and still not fall off. This may sound silly, but it isn't. In a training environment, it can be helpful to go into a bad place of pain and burn and not fear collapsing onto hurty tarmac.
With a Turbo, you really need a programme and you need to stick to it. Vary it if you can, as Turbos are even duller to use than rollers. You can get much more resistance from a Turbo, so you can go for Wattage or you can spin to crazy speeds or both...
If I had to have one or the other, it would be the Turbo.
With both gizzmos, you MUST keep the sessions shortish and you need a good, prepared session to stick to. There are billions on the Web, often pyramidish in form. 45 minutes including warm-up and cool-down is quite enough for me. Both machines will drive you mad if you just get on and pedal for x minutes.
Caveat: I am not a serious racer and never have been. Other views may vary and will probably be more helpful.
Both machines are inferior to a nice ride on a nice bicycle along a nice road. They are training devices, not a form of foul-wather cycling.
.