Heya, I'm not one to specialise in medicine particularly, but speaking for dentistry (which is mostly similar in some cases), I think an irish degree does hold a little bit more international weighting over a british degree. For instance, if I wanted into work in Canada, a BDS degree would not actually be recognized at all by the Canadian dental body, so that's more hoops to jump through in terms of beaucracy and in terms of doing the two extra years required before I can qualify there. On the other hand, an Irish dental degree is actually recognized, so that just means there are fewer applications and exams that I've got to do (even if it's mostly the same).
In terms of foundation training, I don't think that particularly matters as of now, (I could be wrong). In the UK, for medicine, everyone takes the SJT (and in the future, the UKMLA), where your background is basically anonymised and your placement is given based on how you score in the test. Irish medical graduates, do not participate in the same system and placements are allocated places, depending on a different exam (which I'm not sure of), and training placements are done in Ireland. A doctor with a medical degree from the UK will have to take licensing tests to practice in Ireland, and a doctor with a medical degree from Ireland will have to take licensing tests to practice in the UK.
Of course, there are places that may have better international standing than others. A medical degree from Oxford, generally will sound better than a medical degree from say the University of Limerick, and likewise a medical degree from Trinity College Dublin will generally sound better than a degree than one from say Anglia Ruskin. Depending on where you'd want to work in the future that's something to consider as well (obviously, people say "all degrees are the same", and yes, whilst that's true within the UK, it will have a different international standing depending on where you graduate) If you're looking into potential avenues I would highly recommend you talk to doctors who have qualified overseas and see what they say. I'm not sure what it would be like to work in India, but each country will recognize degrees separately so each country is a separate issue.
There are also exams that you can take on the side. Say a medical doctor in the UK wanted to work in the US. Since the GMC wants to stop doctors from leaving the NHS they actually didn't apply for WFME accreditation, it's become a lot harder for UK medical graduates to work there, to the extent where it is pretty much impossible as to qualify in the US you would need a WFME accreditation. However, medical graduates from Ireland do have WFME accreditation so licensing exams can be taken, in the event you wanted to do residency training there. So again, it really depends on where you'd want to go.
Note that by Ireland, above I am referring to The Republic of Ireland, which does not include Northern Ireland. Everything that happens in Northern Ireland is part of the UK system, unless you are an ROI national, where in some cases you can be allocated specialty training spots within Ireland where you can gain qualification there (for dentistry, I'm not entirely sure about medicine). The only university where this is even remotely possible would be Queen's University Belfast. You should try and do more research on that before proceeding on medical schools at either country. As an Indian national, you'd be paying international fees so that doesn't really matter in terms of tuition.
*If anyone sees this and has anything to change please do correct me because there are things that I'm pretty sure I missed but this is just a generalised view