They both work well for holding arrows but each has it's pros and cons.
Slide-ons are very solid but mount on the limbs near the riser fadeouts which for some can affect limb performance and shot results. They are also heavier, sometimes ALOT heavier, than most strap-ons. Some shooters say they like the extra stabilizing effect of the slide-on weight, but others find all that weight (hanging on one side of the bow) to be a problem that affects their shooting, especially regarding bow torque and if using very light (low mass) bows.
Strap-ons are usually lighter than slide-ons...but sometimes can vibrate and make more noise because of it. If used alot they also have parts (like rubber or velcro straps) that may need replacing. They are removable, but some are not as easily removed or mounted as others so if you will have yours on/off alot be sure to pick a model that accomodates 'quick and easy'.
Personal choice really.