Interest in fibers or strips of single crystalline scintillators is increasing for their possible applications in fine-segmented particle detectors for particle physics experiments as well as γ-ray detectors for medical diagnoses. We compared 2×2×100mm3 strips of Gd2SiO5(GSO):Ce, Lu1.9Gd0.1SiO5 (LGSO):Ce, and Lu3Al5O12(LuAG):Pr single crystals for 0.511MeV γ-rays with respect to the effective light attenuation length λa, light yield LY, FWHM energy resolution ΔE/E and rms position resolution σ(z) of the injection position z along the length. The obtained result was (λa, LY, ΔE/E, σ(z))=(128mm, 380phe/MeV, 17.7%, 8.7mm) in GSO:Ce, (509mm, 1760phe/MeV, 12.2%, 10.9mm) in LGSO:Ce, and (171mm, 690phe/MeV, 15.0%, 8.9mm) in LuAG:Pr. The z position was obtained independently from the pulse height ratio as well as the timing difference between both ends of the strip. The latter method gave comparable or even smaller σ(z) than the former only in LGSO:Ce having both large LY and fast rise time. The λa in the 100mm long GSO:Ce strip was found to be twice as large as that in the 200mm long one [1] with the same cross-section. To obtain good ΔE/E and σ(z), large light yield, fast rise time, and moderately large attenuation length are important for the scintillators.