I usually do both. Bionics offer less bonuses but are more reliable. (Integrated toolset, though, is a must for any char.) And considerable stat bonuses can be acquired only from mutations. Also, portal berry mutation heavily outweighs any bionic.
The trick with optimizing mutations is either using targeted mutagens or brewing up liters of regular mutagen, then drinking it a lot until the benefits outweigh the downsides. In any case, one can always use purifier to revert to square one. This is done much much easier with Robust Genetics, and should be avoided without.
Obviously, doing all this requires raiding a couple of labs and having cooking trained to 8-10. So this comes later in game, compared to bionics.
Also, with enough time, tools, and zombie hordes (or a slime pit nearby) you can make mutagen from zombies/blobs, wood and water (logs --> charcoal --> lye --> salt --> salt water --> bleach; bleach + lye + tainted meat/blob glob = mutagen). So go ahead, cut up some trees, weld a couple of charcoal kilns and prepare for fun.
One can also go nuts and waltz around hazmat sarcophagi with Robust Genetics and hope for the best, but good luck shedding all these rads after.
My preferred mutation sets are bird (for pure ranged builds), lizard, cephalopod (for melee brawlers) and alpha. Medical is fine too, but some post-threshold stuff ruins it. Btw, crafting alpha is heavily nerfed in trunk and requires, like, twice as much materials to brew, though it offers a pretty nice quest (going to fungaloids for tainted veggy or triffid groves for buds, and finding a waste treatment plant or a slime pit).