There are at least 3 possible reasons for you seeing a difference between results from these models:
One or both of your attempts to fit this model did not converge, and/or your effective sample size is so small that random sampling error is having a large impact on your inference. If you have already checked to ensure convergence and sufficient effective sample size (for both models) then you can rule this out.
You are seeing small differences in the posteriors due to the random sampling inherent to MCMC in otherwise converged results. If these differences are big enough to cause a meaningful difference in inference then your effective sample size is not high enough - so just run the models for longer and the difference should reduce. You can also set the random seed in JAGS using initial values for .RNG.seed and .RNG.name so that successive model runs are numerically identical. If you run the models for longer and this difference does not reduce (or if it is a large difference to begin with) then you can rule this out.
Your model contains a node for which the default sampling scheme changed between JAGS 4.2.0 and 4.3.0 - there were some changes to sampling schemes (and the order of precedence for assigning samplers to nodes) that could conceivably have changed your results (from memory I think this affected GLM particularly, but I can't remember exactly). However, although this may affect the probability of convergence, it should not substantially affect the posterior if the model does converge. It may be contributing to a numerical difference as explained for point (2) though.
I'd recommend first ensuring convergence of both models, and then (assuming they did both converge) looking at exactly how much of a difference you are seeing. If it looks like both models converged AND the difference is more than just random sampling variation, then please reply here and/or update your question (as that shouldn't happen ... i.e. we may need to look into the possibility of a bug in JAGS).
Thanks,
Matt
--------- Edit following additional information added to the question --------
Based on what you have written, it does seem that the difference in inference exceeds what might be expected due to random variation, so there may be some kind of underlying issue here. In order to diagnose this further we would need a minimal reproducible example (https://stackoverflow.com/help/minimal-reproducible-example). This means that you would need to provide not only the model (or preferably a simplified model that still exhibits the problem) but also some data to which we can fit the model. If your data are too sensitive to share then this could be a fictitious dataset for which you also see a difference between JAGS 4.2.0 and JAGS 4.3.0.
The official help forum for JAGS is at https://sourceforge.net/p/mcmc-jags/discussion/610037/ - so you can certainly post there, although we would still need a minimal reproducible example to be able to do anything. If you do so, then please update both posts with a link to the other so that anyone reading either post knows about the cross-posting. You should also note that R2jags is not officially supported on the JAGS forums, so please provide the minimal reproducible example using plain rjags code (or runjags if you prefer) rather than using the R2jags wrapper.
To answer your question in the comments: in order to obtain information on the samplers used you can use rjags::list.samplers() eg:
library(rjags)
# LINE is just a small example model built into rjags:
data(LINE)
LINE$recompile()
# $`bugs::ConjugateGamma`
# [1] "tau"
# $`bugs::ConjugateNormal`
# [1] "alpha"
# $`bugs::ConjugateNormal`
# [1] "beta"
