The degree of linear polarisation of signals varies from weak to strong between different pulsars. The Vela (J0835-4510) signal is almost 100% linearly-polarised. In contrast, B0329+54 is moderately linearly-polarised. During the peak of the pulse the degree of linear polarisation for B0329+54 is only around 25%. The post-pulse shows a higher degree of linear polarisation at around 75%.
What this means for the strongly linearly-polarised Vela signal is that if, at any instant, the orientation of a linearly-polarised antenna is orthogonal to the incoming signal then a loss of many dBs occurs. For B0329+54 the cross-polarisation loss is about 1 dB due to the low degree of linear polarisation.
Note that the relative angle between an observatory linearly-polarised antenna arranged for 'horizontal polarisation' and a linearly-polarised signal fixed in orientation from interstellar space varies with time and location on Earth due to geometrical effects as well as (primarily at lower frequencies) Faraday rotation. Therefore, the term 'horizontal polarisation' w.r.t. to extraterrestrial objects is largely meaningless (see 'spatial polarisation' in EME terms).
However - the orientation, or the position angle (PA), of the radiation from a pulsar is not fixed in orientation, but swings through a typical PA S-curve during the pulse on-time. In the case of Vela, the PA swings through more than 90 degrees over a few milliseconds. The worse-case scenario for Vela is where, by an unfortunate combination of the aforementioned factors existing at the time of the observation, the incoming signal swings to be cross-polarised with the linearly-polarised antenna right at the time of the peak of the pulse. Much attenuation of the signal will occur. The best case is the reverse situation where the incoming signal polarisation lines up with the antenna polarisation at the peak of the pulse. Therefore, a receiving system which has only one linear polarisation might see a large variation in received signal from Vela at different observation times.
For B0329+54, because the degree of polarisation is much less, the above polarisation effects are much milder and will most likely be hidden by the much larger variations in signal strength due to scintillation for that pulsar. Using linear polarisation is not critically important for this pulsar - however, the local orientation (horizontal, vertical or somewhere in-between) might be advantageously adjusted to be the least sensitive to local RFI.
To counteract the effects of cross-polarisation on the strongly linearly-polarised Vela signal, a two channel system with orthogonal polarisations can be used, as when cross-polarisation occurs in one channel, in-line polarisation occurs in the other.
Circular polarisation (CP) might be another solution for strongly-polarised pulsars (such as Vela). The equal response to all polarisations will eliminate cross-polarisation attenuation variations. A linearly polarised antenna might, at times, produce a signal strength 2 dB or so better than a CP antenna during the best inline-polarisation conditions, but for a significant percentage of the observations, will produce a signal strength similar to, and in some cases, much worse than the CP antenna. It is probably a philosophical argument as to which case is the better.
In general, as the relative degree of linear polarisation varies across pulsars, trying to optimise the receiving system in terms of polarisation options is probably not an overly useful exercise compared to other system factors.
Getting to know your target pulsar and understanding what each characteristic means is an important aspect of successful amateur pulsar detection efforts.