The direction-of-arrival (DOA) of sound sources is an essential acoustic parameter used, e.g., for multi-channel speech enhancement or source tracking. Complex acoustic scenarios consisting of sources-of-interest, interfering sources, reverberation, and noise make the estimation of the DOAs corresponding to the sources-of-interest a challenging task. Recently proposed attention mechanisms allow DOA estimators to focus on the sources-of-interest and disregard interference and noise, i.e., they are signal-aware. The attention is typically obtained by a deep neural network (DNN) from a short-time Fourier transform (STFT) based representation of a single microphone signal. Subsequently, attention has been applied as binary or ratio weighting to STFT-based microphone signal representations to reduce the impact of frequency bins dominated by noise, interference, or reverberation. The impact of attention on DOA estimators and different training strategies for attention and DOA DNNs are not yet studied in depth. In this paper, we evaluate systems consisting of different DNNs and signal processing-based methods for DOA estimation when attention is applied. Additionally, we propose training strategies for attention-based DOA estimation optimized viaa DOA objective, i.e., end-to-end. The evaluation of the proposed and the baseline systems is performed using data generated with simulated and measured room impulse responses under various acoustic conditions, like reverberation times, noise, and source array distances. The best-performing systems are also evaluated using measured data. Our experiments show that DNNs used for DOA estimation are biased to the spectral source characteristics and the spectral attention distribution used during training (e.g., spectrally flat/sparse). We also show that this bias in the DOA estimator can be avoided if signal-processing methods are used in combination with attention. Overall, DOA estimation using attention in combination with signal-processing methods exhibits a far lower computational complexity than a fully DNN-based system; however, it yields comparable results.