I personally find results are very similar when you use paired and unpaired tests. Yet, my recommendation, built upon studying quite extensively the topic, and following authoritative sources, such as this one from Austin, is now to use tests that recognize the clustering features of the dataset.
Thus, if I am using propensity score quantiles (eg quintiles), or propensity matched pairs, I routinely use meglm or xtgee in Stata, for continous or categorical variables, and stratified Cox proportional hazard analysis for survival analysis.
Specifically, the following excerpt, also from Austin, is very clear:
When estimating the statistical significance of treatment effects, the
use of methods that account for the matched nature of the sample is
recommended (Austin, 2009d, in press-b). Accordingly, McNemar's test
was used to assess the statistical significance of the risk
difference. Confidence intervals were constructed using a method
proposed by Agresti and Min (2004) that accounts for the matched
nature of the sample. The number needed to treat (NNT) is the
reciprocal of the absolute risk reduction. The relative risk was
estimated as the ratio of the probability of 3-year mortality in
treated participants compared with that of untreated participants in
the matched sample. Methods described by Agresti and Min were used to
estimate 95% confidence intervals.
We then estimated the effect of provision of smoking cessation
counseling on the time to death. Kaplan-Meier survival curves were
estimated separately for treated and untreated participants in the
propensity score matched sample. The log-rank test is not appropriate
for comparing the Kaplan-Meier survival curves between treatment
groups because the test assumes two independent samples (Harrington,
2005; Klein & Moeschberger, 1997). However, the stratified logrank
test is appropriate for matched pairs data (Klein & Moeschberger,
1997).
Finally, we used a Cox proportional hazards model to regress survival
time on an indicator variable denoting treatment status (smoking
cessation counseling vs. no counseling). As the propensity score
matched sample does not consist of independent observations, we used a
marginal survival model with robust standard errors (Lin & Wei, 1989).
An alternative to the use of a marginal model with robust variance
estimation would be to fit a Cox proportional hazards model that
stratified on the matched pairs (Cummings, McKnight, & Greenland,
2003). This approach accounts for the within-pair homogeneity by
allowing the baseline hazard function to vary across matched sets.
