Neurons in the primary visual cortex respond to oriented stimuli placed in the center of their receptive field, yet their response is modulated by stimuli outside the receptive field (the surround). Classically, this surround modulation is assumed to be strongest if the orientation of the surround stimulus aligns with the neuron's preferred orientation, irrespective of the actual center stimulus. This neuron-dependent surround modulation has been used to explain a wide range of psychophysical phenomena, such as biased tilt perception and saliency of stimuli with contrasting orientation. However, several neurophysiological studies have shown that for most neurons surround modulation is instead center dependent: it is strongest if the surround orientation aligns with the center stimulus. As the impact of such center-dependent modulation on the population level is unknown, we examine this using computational models. We find that with neuron-dependent modulation the biases in orientation coding, commonly used to explain the tilt illusion, are larger than psychophysically reported, but disappear with center-dependent modulation. Therefore we suggest that a mixture of the two modulation types is necessary to quantitatively explain the psychophysically observed biases. Next, we find that under center-dependent modulation average population responses are more sensitive to orientation differences between stimuli, which in theory could improve saliency detection. However, this effect depends on the specific saliency model. Overall, our results thus show that center-dependent modulation reduces coding bias, while possibly increasing the sensitivity to salient features. NEW & NOTEWORTHY Neural responses in the primary visual cortex are modulated by stimuli surrounding the receptive field. Most earlier studies assume this modulation depends on the neuron's tuning properties, but experiments have shown that instead it depends mostly on the stimulus characteristics. We show that this simple change leads to neural coding that is less biased and under some conditions more sensitive to salient features.